In a nutshell (and generally speaking):
The mystery usually has the murder (or other disaster) occur at the beginning of the story, and the rest of the novel deals with the hero finding out whodunnit. Big on character, how s/he figures things out, interacts, foils the baddies, shows off intelligence.
The thriller usually has the murder (or other disaster) looming throughout the novel till the very end, and the hero has to stop it. Big on action, how s/he overcomes the obstacles that the villain creates to foil the hero from stopping the murder (or whateva), and the murder usually is stopped.
The suspense, IMO, is just another word for the thriller, since a lot of thrillers are listed as both. But if you want to get nitpicky, I have read stories where one murder (or disaster) occurs at the beginning, and the hero is not only trying to figure out whodunnit, but is trying to prevent another (bigger) such calamity from occuring, which climaxes at the end; or the hero is in mortal danger throughout the rest of the novel as s/he tries to figure it out. I suppose this could be considered the suspense, for lack of a better term. But look at most of Alfred Hitchcock's movies... they were all termed "suspense" back in the day, and are today just as often referred to as thrillers. In most of his movies, something very bad is apparently going to happen unless the hero prevents it, or (as in REAR WINDOW), something bad does occur, and the hero becomes endangered while trying to figure out whodunnit.
The horror story... can't help you there. I know one when I see it, but I haven't read enough to define it as clearly as the others. I suppose you could use elements from the mystery or thriller, and instead of a "simple" murder or such, substitute an element of the supernatural (ghost, monster, Rosie O'Donnell) and it might be considered horror. But I'm just specultaing.
