The reverse-puzzling tag is for:
A question where you must identify a puzzle based on a reasoning to solve it.
The puzzle-identification tag is for:
A question inquiring about the name or nature of a specific puzzle, given its description.
From the tag wikis, there doesn't seem to be any difference in meaning. From the usage patterns of the two tags so far, however, it looks like puzzle-identification has been used for questions where the OP doesn't know the answer (e.g. What's the name of this puzzle, which consists of small cubes connected by elastics? and What is this magic trick with 6 cards featuring numbers between 1 and 60?) while reverse-puzzling has been used for questions which are puzzles in themselves, such as Reverse Puzzling and The missing page of Adrian Puzzlinger.
Is this a distinction worth making?
If so, let's rewrite the tag wikis to clarify the usage difference between the two tags, and ensure that all questions in these two categories are tagged correctly.
If not, let's synonymise the two tags.