co-occur vs overlap

co-occur is not a noun while overlap is a noun.

Word	Noun	Adjective	Verb	Adverb
co-occur	No	No	Yes	No
overlap	Yes	No	Yes	No

As verbs, overlap is a hyponym of co-occur; that is, overlap is a word with a more specific, narrower meaning than co-occur:

co-occur (noun)	overlap (noun)
	a flap that lies over another part
	the property of partial coincidence in time
	a representation of common ground between theories or phenomena

co-occur (verb)	overlap (verb)
go with, fall together	extend over and cover a part of
	coincide partially or wholly