In a nutshell, what's the difference between writing a mystery and a suspense?
First of all, a mystery deals with a crime either with or without a dead body as a victim. Traditional mystery begins *after* the murder, and follows the "investigator" whether amateur, professional or a combination on the journey through clues, interviews, etc. until the "puzzle" is solved, justice is served and order in the world is restored.
A suspense begins with a problem and follows more of a hero/heroine's journey pattern. All the action happens to the hero/heroine; they may have helpers and usually must learn a new skill or rely on something to help them overcome obstacles and resolve the situation.
Recommended reading: Carolyn Wheat's How to Write Killer Fiction