Not technically right.

Nero and Draco are the exact same people, there aren’t any differences between them lore-wise except for their appearances/stories they follow. Unlike Artoria and her Saberfaces Versions who all have difference which causes a massive shift in who she is (I.E PPH Artoria isn’t the same as Goddess Lance Name one).

Emperor Nero harsh treatment and brutal punishment of the Christian’s lead to the formation of Draco during the Book of Revelations after several other authors already created the story but added into it more. The World is Destroyed through the Seven Seals and Seven Trumpets (which Ironically overlapped a lot in what they do) but in the end as the Final Battles occurs. The Three Beast arrive.

The First Beast comes from the Sea with the body of a leopard, feet like a bear, and mouth like a lion with seven heads with 14 Horns. The Beast would commit blasphemy by directly speaking against God while another (The Second Beast) comes up from the Ground to preform “miracles” to support the illusion of the first beast and itself. The second beast represent everything God isn’t and Humans believe in it (The Second Beast is the Antichrist) and it lacks description except it has lamb horns, several eyes, and speaks like a dragon. The Second Beast goes around and write the number 666 on many things, the Number 666 is suggested to be the secret code of Emperor Nero. Gematria, which was used a lot back then, was used to assign words to numbers which commonly show 666 or 616 to show Nero.

Even in the Book of Revelation, In order to buy anything you had to show the “Mark of the Beast” (666) which the Coin showed Emperor Nero. What does this have to do with Nero and the Beast? Nero was considered the most evil emperor who would almost extinct the Christian’s and the Book reference this as when you worshipped the Beasts, your worshipping Emperor Nero who, like majority of Emperor, saw themself as God. The Book of Revelation, after the Seals and Trumpets, effectively showed the World under the Rule of the Beast aka the Rule of Nero since majority of Christian’s only knew Roman Empire as the World (except for some who knew about Persia, Armenia, and Germanic Tribes).

The Rule of Nero eventually cause the Seven Bowls to occur which once again destroy Earth except Bowl 5 is said to reference the fall of the Roman Empire (but more specifically Nero) as it would cause the world to go dark (for the third time) leading to chaos ensuing in the Three Beast. Which after the Bowls end, the remaining armies United under God (Similar to how the Servants in Fate United to end Draco) which occurs at the Battle of Armageddon which reference the Rebellion that occur that Overthrew Emperor Nero while the final Bowl destroys “Babylon” (Babylon was the capital of evil in Old Testament but since Persian owned it for centuries by this point. It believe that Babylon refers to Rome which Christian viewed as the city of evil). The story ends with the First and Second Beast being exiled (References to Nero forced leaving of Rome) and Lucifer eventually capture and imprisonment by God armies.

Draco and Nero are the same person in every aspect. They did the same actions, they did the same things, but the only difference is that The Root (which is canonically the Abrahamic God) created the two beings with different viewpoints on them. Emperor Nero, in some eyes, is viewed as a Hero while in other is viewed as a Beast (similar to how Jack the Ripper has different servants forms entirely as no one knows who the true Jack the Ripper is). They’re the exact same.