I write mysteries. Red herrings (love that visual - where did it arise, anyway?), lots of possible suspects, all kinds of twisted paths, lead the reader to a hopefully logical ending, where s/he can say "But of course he's the killer!". Those mysteries that drag a killer out of thin air, a character who doesn't appear until the last chapter, drive me nuts. But it has always seemed to me that the joy of a mystery happens as the reader follows the clues along with the fictional sleuth. Then voila! (Not viola, as in the musical instrument, but the French word that the iPad doesn't accent for me.) The crime is solved!
Thrillers, on the other hand, need a known bad guy right up front. The reader is made well aware of the level of danger involved in stopping this evil. Stakes are high, because the readers, along with the protagonists, are biting their nails, praying the evil they understand is out there won't succeed. Often, the protagonist's fear and dread are aggrandized as the reader is sucked into the driving need to stop the baddies. When the reader knows the consequences of failure as well as the protagonists, you have a thriller.
Sure, mysteries can be tense nailbiters. Will the unknown bad guy strike again? They can also be more leisurely, character studies dipped in a poisoned pen. Or they can be cozies, with humor and silliness. Thrillers, though, are never funny or cute. They are driven by action and the need to stop the known enemy.
That's my take on the difference between the two genres. What's yours?