I propose that one of two different things be done: either ❶ merge genitive into possessive and make it a tag synonym, or else ❷ arrive at some reasonable description for genitive that makes it distinct from possessive, and to have this description writ into its tag wiki.
I favor the merge-and-synonymize solution myself, because I do not believe that there is an English “genitive” that differs in any meaningful way from a possessive. I may be wrong, though, and I would be glad to be shown that the second solution would therefore be preferable.
Even when discussing pronouns instead of nouns or noun phrases, which is the only place where something of the Old English case system is preserved, I do not see where it makes any sense to use one word over the other.
I am thinking that in all these cases, one could call it a possessive without losing any nuance that might be had by calling it a genitive:
- possessive noun phrase: the King of Spain’s hat
- possessive noun: Billy’s hat
- possessive determiner: my hat
- possessive pronoun: mine
- “double”-possessive: a friend of Bill’s, a friend of mine
Perhaps “genitive” might arise when contrasting the “Norman genitive” (the king of Spain) with the “Saxon genitive” (Spain’s king), but I don’t see any strong advantage to keeping separate tags.
Plus even if we somehow come up with a nuanced distinction between the two terms genitive and possessive, I don’t believe most users of the site would recognize that distinction, and so doing so would be counter-productive.