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.
Based on the wiki descriptions, I propose that detective should be made into a synonym of mystery, as the wiki descriptions indicate that detective is a proper subset of mystery.
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.