Why do villains tend to be the impact characters in horror stories? Also, are there any examples of horror that come to mind in which the Influence Character is not the Villain or Antagonist?

The Villains, who are also often the Antagonists, are frequently the Influence Character because the IC is one of the few characters whose perspective must exist until the end of the story. So the Villain is often the IC in horror stories because everybody else is dead or removed from the scene.

There are a couple of movies that come to mind where the Villains (or monsters) are not the IC, though several of them are mixed genres such as Horror/Fantasy, Horror/SciFi, or Horror/Drama"

•  The Reaping: IC: The little girl; Villain: Doug (and the townsfolk)
•  Pitch Black: IC: Riddick; Villians: Monsters
•  Aliens: IC: Newt; Villains: Aliens/Mother Alien
•  Stir of Echoes: IC: Ghost (Samantha Kozac); Villians: The neighbors that killed her and covered it up.
•  Edge of Darkness: IC: Hit Man; Villains: Corporate and government cover-up guys
•  30 Days of Night: IC: Stlla Oleson (love interest); Villains: Vampires

Granted, these are the exceptions rather than the rules, and each of these seem to be more than just "horror" movies.

Don't they mean the same thing?

Do not confuse an archetypal Antagonist in Dramatica with a classical "Villain." A Villain is a non-Dramatica term often used to describe a character responsible for causing or doing things the audience doesn't like (i.e. the 'Bad Guy') -- usually to characters the audience likes. A Dramatica Antagonist, on the other hand, is the character trying to prevent the overall goal from coming to pass or being achieved. Quite often characters are both the Antagonist and the Villain (e.g. Dr. Evil in Austin Powers, or the Terminator in The Terminator). Other times an Antagonist will be more complex than a simple Villain (Jane Hudson in What Ever Happened to Baby Jane?, or Buddy in Lonestar), or a Villain may be the Protagonist (Richard III in Shakespeare's Richard III).