The setting was written in 1996 with Mahoutsukai no Yoru/Kara no Kyoukai.
Also the other half of the setting is all about vampires, and it's definitely kind of like White Wolf Vampire, but not close enough to look intentional.
Sort of, the setting is the same but none of the series are actually in continuity with each other. Even Fate/Zero isn’t actually the same universe as Fate.
If they did that it’d restrict the story too much - Nasu loves setting rules about how the magic stuff works, but he only does it so he can break them later to make someone look cool. That’s why he’s the world’s best fantasy writer.
Also the other half of the setting is all about vampires, and it's definitely kind of like White Wolf Vampire, but not close enough to look intentional.