I think
attributive genitive is the term I was looking for. If you run
this BNC search, and then drill down to the actual text, you'll see that the corpus text doesn't have an apostrophe (and this is not the same as a Google search, which just
ignores punctuation). In some cases, as I said in the OP, possession is clear - as in "summer's edition"; but in expressions like "summers day" the sense of possession is weaker - so weak that many users omit the apostrophe.
b
A great many genitives have nothing to with "possession". For example,
a s
ummer's day means a 'day typical of those occurring in summer', not a day possessed by a summer. And the same with
fisherman's cottages, which doesn't mean cottages owned (or possessed) by fisherman, but cottages typical of those lived in by a fisherman. Similarly,
an old people's home means a home typical of those lived in by old people, not a home that is owned by old people.
I can't see any semantic difference in terms of possession, or rather the lack of it, between
summer's edition and
summer's day. Neither of them permit a paraphrase with
possess in the way that
her car can be paraphrased as
the car she possesses. I can't account for those occurrences where the genitive
' has been omitted - they appear to be simple errors.