Can anybody suggest a sentence that can be used to describe the difference, and which could be used in the tag wiki of one of the tags?
I doubt there's any objective distinction. But for the purposes of ELL I think all it comes down to is that questions tagged grammaticality ask if some particular construction is grammatical or not.
They're just a particular subset of all questions concerned with grammar, so it doesn't really matter whether they're explicitly tagged with that as well (if not, it's implicit anyway). By the same logic, there's no reason for the grammar tag description to be worded so it excludes questions about grammaticality.