I see detective and mystery used with a high degree of overlap. Namely, for puzzles which describe a scenario and then ask you to deduce the culprit or cause. To be fair, they do have differing wikis:
- Detective: "For puzzles that involve solving a crime."
- Mystery: "A puzzle that involves figuring out what happened with regards to a certain incident."
But in practice, almost any question tagged with one could be tagged with the other.
If you have an opinion and the ability to do so (it requires at least 1250 rep and a score of 5 in the tag), please vote on the proposed synonym.