Cleo Soul is Neo Soul
Yes, but I'd Acid Jazz wasn't only party music, s lot was but not exclusivly
It was also a record label (Gilles P) which helped define the term in real time. Acid Jazz came from the Rare Groove and older well established Soul scene when that came up against a Jazz Dance scene focussed on Dingwalls where all of a sudden we were dancing to Blakey and others. Younger musicians blended the influences to varying degrees. Acid Jazz then spread out definitely to Japan, see UFO as early adaptors
And the Jazz Cafe evolved from a predominantly Jazz venue to one that presented all of the music we're talking about and as @Rabshakeh says, in his youth, not mine the Jazz acts were a lot less common.
I don't see Acid Jazz morphing into Neo Soul, Acid Jazz largely faded whilst Neo Soul emerged in parallel, we haven't mentioned Maxwell have we?