Villain Antagonist
A Villain Antagonist is when the villain and The Antagonist are the same person. This combination of roles is extremely common, though probably not as much so as the inverse that often opposes this character, the Hero Protagonist. Simply put, the central character's opponent is also an established force for evil within the universe. This role is used most often in classical myths and heroic legends, since these tales are usually a story of conflict between the forces of good and evil. It's common to see these characters ether cause or be personifications of real-life issues in order to fulfill the audience's desire to see these problems dealt with when this character loses to The Hero. This character's primary role, generally speaking, is to provide conflict while giving the audience reason to root for the Hero Protagonist to win that conflict. Very common in stories with Black and White Morality.
No examples, please; this is an Omnipresent Trope.