There are 36 questions tagged apocalypse, only twelve of which are not also tagged story-ID. Of those twelve, most seem to be either about apocalypses in specific works of fiction, or general questions about the post-apocalyptic genre. One is about a specific character called Apocalypse; one should be a story-ID question but isn't tagged properly; and a few of the older ones are about particular post-apocalyptic works but not specifically about the apocalypses therein.
There are 134 questions tagged post-apocalyptic, only twelve of which are not also tagged story-ID. Of those twelve, two are actually story-ID questions but not tagged properly, two are specifically about the apocalypses in particular post-apocalyptic works, and the rest seem to be generic questions which are about post-apocalyptic works but not specifically about apocalypses.
Should we merge these tags - and if so, which way?
Normally I'd say post-apocalyptic is a better name for the tag - it describes a genre of speculative fiction, rather than just a type of event featured in such works. But the evidence above, gleaned from looking at the actual questions, suggests that apocalypse is actually used marginally more sensibly. Ignoring story-ID, I think 7 apocalypse questions and only 2 post-apocalyptic questions should have the tag. Or should we say this is one of those tags which isn't really useful except on ID questions?
Note that merging the two tags wouldn't require any bumping of questions to the front page, and editing the few badly tagged questions only requires a small amount.