Back when Marce hosted Thrill Week (see here), I found that I couldn't quite distinguish the differences among these genre: mystery, thriller and suspense.
I came across this article today that talked about it. What do you think of the explanation? In short, this is the summary (copy/paste from the article):
mystery: the main character is occupied in tracking down the truth about an event, usually a murder. If the protagonist is in any danger, it is usually moderate, and becomes a problem only as the detective approaches the truth.
thriller: the protagonist is in danger from the outset.
suspense: the main character may become aware of danger only gradually. In a mystery, the reader is exposed to the same information as the detective, but in a suspense story, the reader is aware of things unknown to the protagonist. The reader sees the bad guy plant the bomb, and then suffers the suspense of wondering when or if it will explode.
Does that help you?