You're thinking actual vampire bats. The corpses vampire folklore was based on were simply old and decomposed just enough that the skin had dried, pulled taut and shrunk, giving the false impression that the hair and nails were growing, and the gums had followed a similar process, leading to more of the tooth roots being exposed. I'm not sure the idea of them having specific "fangs" was originally part of the folklore so much as a general feeding on blood.
