Vampire/original fiction rant/question

WARNING: vampire musings, as in undead, so probably more than a bit squicky.

Question. If you have what amounts to a vampire story in which the vampires in question are not, in fact, dead/undead ... do they actually count as vampires? Because I'm not sure. Possibly I'm just talking about systematised demonic possession, instead ...

( Have a rant about the mechanics of vampire stories, leading to an attempt to design one myself, leading to a question. Any help/opinions would be appreciated -_-; )