On the Sisters in Crime discussion list, a writer is asking for a simple way to distinguish mysteries and thrillers, and also asks whether mysteries "always have less suspense than thrillers." Here's my reply:
A young Dane dons an antic disposition to investigate his father's murder. That retrospective look at something that's already happened makes Hamlet a mystery, though at the time, of course, Shakespeare didn't know he was writing a mystery. (Which accounts for the play's many frustrating failures to observe genre conventions!)
Driven by his ambitious wife, a Scotsman plots to kill the king and steal the throne, and then has to live with the consequences, as others plot to stop him. That contemporaneous narrative focused on events as they happen or as they are about to happen makes Macbeth a thriller.
The question about the suspensefulness of mysteries versus thrillers is an interesting one. My feeling is that the answer depends less on the elements of the narrative and more on the preferences of the reader, i.e. where you get your kicks. If you prefer the ticking time bomb, chases and explosions, then thrillers are for you. If you dig the intellectual challenge of puzzling out whodunit, howdunit and whydunit, then you probably prefer mysteries.
The main thing to remember, though, is that the two forms borrow shamelessly from each other. Many great mysteries employ thriller tropes. So, for example, the cat and mouse games that protagonists and antagonists play are present in both thrillers and mysteries. Great thriller characters employ ratiocination to investigate and figure out what's going on.
The elements of mysteries and thrillers work well together and are intimately interwoven in our greatest stories and iconic figures. That's why it makes sense to view both as sides of a single genre rather than two distinct forms of literature. Sherlock Holmes is as likely to be involved in stopping a train wreck as he is to investigate why two trains collided. As long as the game's afoot, we happily follow, regardless of which game we're playing.