The term vampire is used for several kinds of creatures. They each are separate and different, but have a common trait in feeding on other beings in various ways.
The different vampire kinds do not seem to have distinct proper names, instead being called after the organisations heading their kind, the Vampire Courts. There are, according to Jim Butcher, seven vampire courts. Though, besides the Black, Red, White and Jade Courts, the others are "little better than mosquitos". (ref?) Sometimes, the term "anthrophage" (or "human-eater"), is used for them.
The Courts are several organizations of vampires. Each Court represents one of the types of creatures that, although different, are commonly all called "vampires". (ref?)