This post covers everything relevant to dragons as far as the localization is concerned. It is based on a series of reddit posts from April 2018. Quotes include the official English script, my translation, and the official Japanese script in that order.

The Everlasting
The original dragons are denoted as their own species of “old dragons”. (古竜) This is translated inconsistently throughout the localization, but later games come to adopt the term “archdragon” similar to how “archtrees” came to be used for the “old trees”. (古木) For the sake of simplicity, I will use these terms. Ultimately, these two species predate Fire and so are named after the age they originate from.
This particular species of dragon is described as literally “nondecaying”, (朽ちぬ) but this more or less means physically or metaphorically immortal. This is because of their bodies…
Have you heard of Seath the Scaleless? In legend, he turned against the ancient dragons. He became Lord Gwyn’s confidant, was granted dukedom, and was allowed to pursue his research. At the Regal Archives, he immersed himself in research on scales of immortality, the one thing that he did not have… But his very research drove him mad… The Archive became a dungeon, a place for sinister experiments. Now, nobody dare even approach the duke’s forbidden Archives.
By the way, do you know about the white dragon Seath? It is said in legend that he’s a traitor to the archdragons. He became ally to Great King Gwyn, obtained the name of Duke, and was given the freedom to seek, immersing himself in the research of scales of undeath, which he lacked, in the massive Archives… But, that research eventually drove him mad. The Archives became a prison and made a place for horrible experiments. Even now the Duke’s Archives is a forbidden castle no one approaches.
そういえば、白竜シースを知っているか?
伝承に言う、古竜の裏切り者だ
彼は、大王グウィンの盟友となり、公爵の名を得、探求の自由を与えられ
巨大な書庫で、彼にない、不死のウロコの研究に没頭した
…だが、その研究は、やがて彼に狂気をよび
書庫は牢となり、陰惨な実験の地と化した…
今や公爵の書庫は、誰近づくものもない禁域だ
Undead is literally “non-dead” and so has a double meaning of “undead” and “immortal”. For that reason, it is used to refer to the Undead curse as well as the dragons’ stone scales of immortality. This extends to Seath being called a “true Undead” by Logan. As an aside, the Undead Dragons we encounter are actually called “dragon zombies”. (ドラゴンゾンビ)

Dragon scale for reinforcing dragon weapons. Peeled from an ancient dragon.
A dragon is inseparable from its scales, and the transcendent apostles, who seek the perpetuity of the ancient dragons, have crossed the very end of the earth to seek this invaluable treasure.
Scale used to enhance dragon weapons, said to be born from the body of a dragon.
Dragon scales are part of an archdragon’s body, and it is said that the transcenders who seek the eternity of the archdragons are searching beyond the ends of the world.
竜の体から生まれるという
ドラゴンウェポンを強化するウロコ竜のウロコは古竜の体の一部でり
古竜の永遠を求める超越者たちが
世界の垣根を超え探し求めているという
Eternity has (again) a meaning of immortality, something permanent. Dragon worshipers want a piece of this immortality, and game director Hidetaka Miyazaki elaborates on this in interviews. It is not just their stone scales, either…
Created from an everlasting dragon tooth. Legendary great hammer of Havel the Rock.
The dragon tooth will never break as it is harder than stone, and it grants its wielder resistance to magic and flame.
Legendary great hammer of “Rock-like” Havel said to be the tooth of an unperishing archdragon made into a weapon as it was.
This tooth is harder than a rock and never breaks. It also gives the user the power to endure magic and fire.
朽ちぬ古竜の牙をそのまま武器にしたという
「岩のような」ハベルの伝説の大槌その牙は岩よりも硬く、決して折れず
また使用者に魔法と炎に耐える力を与える
Good ol’ Havel proves that the ancient dragons had solid teeth and the same is true for their bones…

A weapon from the soul of the Iron Golem, guardian of Sen’s Fortress who repelled countless heroes who sought Anor Londo.
The Gods fused the power of the soul with the great bones of the dragons, forming an appropriate core for the giant golem.
Weapon born from the soul of the Iron Golem that slaughtered heroes aiming for Anor Londo as guardian of Sen’s Old Castle.
The gods probably formed the mighty golem’s core by combining the magic power of a soul with the bone of an archdragon.
センの古城の守護者として
アノール・ロンドを目指す英雄たちを屠ってきた
アイアンゴーレムのソウルから生まれた武器神々は、古竜の大骨にソウルの魔力を融合し
もって強大なゴーレムの核としていたのだろう
If you want something strong and sturdy, archdragons make for good framework. They represent the immovable stone, unchanging and constant.
Dangerous Sport
Well, things weren’t hunky-dory for the dragons forever, as the Lords proved:
And Seath the Scaleless betrayed his own, and the dragons were no more.
And then, the archdragons were finally defeated due to the treachery of the scaleless white dragon, Seath.
そして、ウロコのない白竜、シースの裏切りにより、遂に古竜は敗れた
The dragons as a whole weren’t “no more” as we encounter plenty on our journey. The archdragon species, however, was defeated and brought to the brink of extinction. They were badly losing to the Lords and then were stabbed in the back, guaranteeing a massacre. The gods were well-prepared:

One of the special rings granted to the four knights of Gwyn, The Hawk Ring belongs to Hawkeye Gough, who led the Greatarchers.
Boosts bow range, so that arrows fly like they were shot by Gough’s great bow, which took down high-flying dragons.
Special ring that was given to the Four Knights of King Gwyn. The Hawk Ring is a thing of “Hawkeye” Gough who led a greatbow unit.
Has an effect that extends the range of bows, and it is said that Gough’s greatbow shot down archdragons in the distant skies.
グウィン王の四騎士に与えられた特別な指輪
鷹の指輪は大弓隊を率いた「鷹の目」ゴーのもの弓の射程距離を伸ばす効果があり
ゴーの大弓ははるか空の古竜を射落としたと言う
Gough was the leader of his own ranged unit and apparently did quite a good job slaying dragons with it.
One of the special rings granted to the four knights of Gwyn. The Leo Ring belonged to Ornstein the Dragonslayer.
This ring strengthens counters with pierce weapons. His lugged spear is said to have sliced a boulder in two.
Special ring that was given to the Four Knights of Gwyn. The Lion Ring is a thing of “Dragon-hunter” Ornstein.
Has effect that boosts that counter attack power of thrusting weapons, and it is said that his cross-spear even pierced rock scales.
グウィン王の四騎士に与えられた特別な指輪
獅子の指輪は「竜狩り」オーンスタインのもの刺突武器のカウンター攻撃力を高める効果があり
彼の十字槍は岩のウロコをも貫いたと言う
Ornstein wasn’t generically cutting boulders in half, he was stabbing dragons. And he had similar success to Gwyn in piercing those scales. But these hunts haven’t stopped humans from worshiping them:
Stone imbued with the power of the dragons. Rite of apostles of the ancient dragons. Gain head of dragon. Emit dragon breath.
The dragon apostles seek transcendence of life itself, attainable by transformation into an ancient dragon. This rite is only one step, but it cannot be reversed until death.
Stone imbued with the power of the unperishing archdragons. Secret rite of the transcenders who pray to the archdragon and try to approach it. Makes human head into that of a dragon and breathes a dragon’s breath.
What the transcenders aim for is the transcendence of life, and for that reason they try to acquire the perfect form of the archdragon. This secret rite is only the gateway to that, but its metamorphosis effect cannot be undone until death.
朽ちぬ古竜の力を宿した石
古竜に祈り、近づこうとする超越者たちの秘儀
人頭を竜のそれとし、竜のブレスを吐く超越者の目指すものは、生命の超越であり
そのために古竜の完全な似姿を得ることである
この秘儀はその入り口にすぎないが
その変態効果は死ぬまで解けることはない
Humans (especially Undead) want that permanent, unchanging immortality the ancient dragons possess, so they will gladly worship one and transform their being. And that means encountering this primordial species…

Descendants?
Hmm… You are a fine trading partner. Rumour it may be, but I have heard of a surviving ancient dragon who resides in this land. A coterie of Undead serves the dragon, as they train to become dragons themselves. Sounds unlikely, but you never know, do you?
Hmm… Well, since you’re a good business partner… I don’t even know if the rumor’s true, but apparently there’s a survivor of the old dragons somewhere in this land. I hear several Undead are serving the archdragon and training to become dragons themselves. If it is true, I definitely want to meet it…
ふーむ…
まあ、君はいい取引相手だからね…
真偽も分からない噂だけど、この地のどこかに、古い竜の生き残りがいるらしい
僅かな不死が古竜に仕え、自らも竜になるために修行しているとも聞くよ
もし本当なら、是非会ってみたいものだねえ…
The first use of old/ancient is a descriptor whereas the second uses the actual term. The NPC itself is dubbed the Stone Archdragon, so is is a member of the species…
An art of the transcendent apostles who pray to the ancient dragons. To be alive is to be vulnerable, and the fiery Gods are no exception. The apostles seek another plane of existence, which transcends life.
Art of the transcenders who pray to the archdragon and try to approach it. Living is a weakness, and even the gods who are persons of fire are no exception. For the goal of the transcenders is apparently to be different from life.
古竜に祈り、それに近づこうとする超越者たちの業
生とは弱さであり、火の者である神々も例外ではない
超越者の目標は、生命とは別のあり様なのだ
These worshipers in the “Path to the Archdragon” (古竜への道) covenant expect the stone dragon to make them everlasting archdragons, and this item it gives is an “archdragon eye”. (古竜の瞳) If it is an archdragon, it should have the power of one, no?

This sword, one of the rare dragon weapons, came from the tail of the stone dragon of Ash Lake, descendant of the ancient dragons.
Its great mystical power will be unleashed when wielded with two hands.
Weapon born from the tail of the Stone Archdragon, descendant of the unperishing archdragons of before that sits in Ash Lake. One of the rare dragon weapons.
It is tinged with strong mysterious power, and that power is unleashed with both hands.
灰の湖に座するかつての朽ちぬ古竜の末裔
石の古竜の尾から生まれた武器
希少なドラゴンウェポンの1つ強い神秘の力を帯びており
両手づかいでその力が解放される
This weapon too is the “archdragon greatsword”, (古竜の大剣) so there is no denying that this beast is a member of the species, stone scales and all. But it is also a “descendant” of them, meaning that you can be born from archdragons and still be one yourself. Which is important since…
This axe, one of the rare dragon weapons, is formed by the tail of the Gaping Dragon, a distant, deformed descendant of the everlasting dragons.
The axe is imbued with a mystical power, to be released when held with both hands.
Weapon born from the tail of the Voracious Dragon, descendant of the unperishing archdragons that became grotesque. One of the rare dragon weapons.
It is tinged with strong mysterious power, and that power is unleashed with both hands.
異形となった朽ちぬ古竜の子孫
貪食ドラゴンの尾から生まれた武器
希少なドラゴンウェポンの1つ強い神秘の力を帯びており
両手使いでその力が解放される
The Gaping Dragon isn’t a “distant” descendant, it is just a descendant like the Stone Archdragon. By that logic, it is also a member of the species, and Miyazaki repeatedly uses it as an example for the archdragon race. So that is two archdragons we have met so far. Who else?

The Atypical
This sword, one of the rare dragon weapons, came from the tail of Seath the Scaleless, the pale white dragon who betrayed his own.
Seath is the grandfather of sorcery, and this sword is imbued with his magic, which shall be unleashed as a wave of moonlight.
Weapon born from the tail of the white dragon Seath, the scaleless archdragon who once betrayed his brethren. One of the rare dragon weapons.
It is the magically-powered crystals of Seath, who is the founder of sorcery, and that power is unleashed as a wave of moonlight.
かつて同胞を裏切ったウロコのない古竜
白竜シースの尾から生まれた武器
希少なドラゴンウェポンの1つ魔術の租たるシースの魔力の結晶であり
その力は月光の波として開放される
Despite his bizarre appearance, Seath too is an archdragon, he just has lots of crystallized moonlight magic compared to his brethren. So even he is not radically different enough on the evolutionary scale to be a separate species.

Ah, hello there. What of Kalameet? He is an ancient dragon. Skyward or no, he will not be put down easily.
Oh, you again. What of Kalameet? He is also progeny of the old dragons. Felling him probably won’t be easy.
ほう、また貴公か。どうだ、カラミットは?
あれも古い竜の末だ。落ちたとて、一筋縄ではいかんだろう
Once again, there is an implication of Kalameet being an archdragon by birth. And his status is reinforced by the following:
This greataxe, one of the rare dragon weapons, is formed by the tail of the one-eyed black dragon Kalameet, the last of the ancient dragons.
The mystical power of its obsidian blade will be released when held with both hands.
Weapon born from the tail of the one-eyed black dragon Kalameet, last survivor of the unperishing archdragons. One of the rare dragon weapons.
Its obsidian blade is tinged with strong mysterious power, and that power is unleashed with both hands.
朽ちぬ古竜の最後の生き残り
単眼の黒竜、カラミットの尾から生まれた武器
希少なドラゴンウェポンの1つ黒曜の刀身は強い神秘の力を帯びており
両手使いでその力が解放される
This “black dragon greatsword” (黒竜の大剣) describes Kalameet as their race’s last survivor. But that’s odd. Even if Seath is excluded because he lacks their everlasting scales, the Stone Archdragon was called the very same “survivor” too! Of course, it may be referencing him being their last survivor from the dragon hunts, and the other two are never confirmed to have been born or at least known about during the DLC’s events, after all.

But that’s not the weirdest thing about the black dragon…
The stray dogs serving the Capra Demon are generally dubbed “Minister’s Black Dog” (公使の黒犬) in the game files, a reference to the fat officials (ministers) from Demon’s Souls. But the ones in its boss room in particular are called “Minister’s Black Dog (machete servant)” (公使の黒犬(ナタの眷属)) with the Capra Demon being the “machete demon”. (ナタデーモン)

What does this have to do with dragons? The dog enemies leading up to Kalameet are called “Black Dog (black dragon servant)”. (黒犬(黒竜眷属)) Weird considering their black and yellow-colored scales match Kalameet. What a coincidence!
This sword, one of the rare dragon weapons, is formed by a drake’s tail. Drakes are seen as undeveloped imitators of the dragons, but in they are likely their distant kin.
The sword is imbued with a mystical power, to be released when held with both hands.
Weapon born from the tail of the wyvern Hellkite. One of the rare dragon weapons. Wyverns are referred to as failures of dragons, but they are still distant descendants of the unperishing archdragons, aren’t they?
It is tinged with mysterious power, and that power is unleashed with both hands.
飛竜ヘルカイトの尾から生まれた武器
希少なドラゴンウェポンの1つ
飛竜は竜のできそこないと言われるが
やはり朽ちぬ古竜の遠い子孫なのだろうか神秘の力を帯びており
両手使いでその力が開放される
While it is translated inconsistently as “drakes” or “wyverns”, they are literally “flying dragons”. This is a species term just like “old dragons”, which makes sense since all the archdragons up until now have had at minimum four limbs and one set of wings while these (actual) distant descendants have had their front limbs and wings fused together.
Side note: Hellkite dragon is “Flying Dragon Hellkite” in the same vein as “Black Dragon Kalameet” and “White Dragon Seath”. Hellkite is its name, not its breed.

As a result, they are failures, good-for-nothings, etc. In fact, dekisokonai is similar in meaning to narisokonai (なりそこない) used to describe failed-to-be dragons. These terms aren’t just used for dragons either.
The serpent is an imperfect dragon and symbol of the Undead. Its habit of devouring prey even larger than itself has led to an association with gluttony.
For a failure of a dragon, the snake, which is a symbol of the Undead, is conversely also known as an extremely greedy creature which swallows prey even larger than its body whole.
竜のできそこないとして、不死の象徴である蛇は
一方で、体よりも大きな獲物を丸のみする
きわめて貪欲な生物としても知られている
Snakes aren’t just “imperfect”, they are disgraces to their apparent lineage. While this is the same description for wyverns, later games change the terminology to narisokonai for presumably consistency. Ultimately though, the meaning isn’t much different. Archdragons evolved into increasingly more pathetic races compared to the earlier generations.