The focus is on the scares. In general, the big evil is well determined. The audience wants to see, almost in a voyeuristic and morbid way, how the victims lose their lives facing the inevitable. In horror, the climax of this confrontation is to escape or to stop the big evil Horror movies "horrify" the audience.
The focus is on solving a mystery A chase of some sort that generates suspense, tension and, well, thrills A large percentage of the time the big evil acts from the shadows In a thriller, the climax is usually to reveal the identity of the big evil or their future plans Thriller movies "thrill" the audience