Uncle Bob recently put together the first (that I've seen) definitive articulation of Test Definitions.
I'm ashamed to admit the number of times I've struggled in conversations to articulate the difference between Acceptance, Functional & Integration tests, that fuzzy layer of stuff in the middle of the testing pyramid.
How much these get mixed and mean very different things to different people has meant any discussion of the testing pyramid is fraught with confusion and misunderstanding.
That's a shame but possibly one of the causes of why it remains the missing layer of testing. If we can't even agree what it is, what hope is there that we could actually implement it.
So for my own benefit (but maybe it might useful to others) I've put together a cheat sheet based on Uncle Bobs definition. (You should read the original article for the actual explanation of each.)
Your definition may differ but it'd be great if we could actually for once just all agree on one. Until I see something better, this is the definition I'm going with.