make hay vs exploit

make hay is not a noun while exploit is a noun.

Word	Noun	Adjective	Verb	Adverb
make hay	No	No	Yes	No
exploit	Yes	No	Yes	No

As verbs, exploit is a hypernym of make hay; that is, exploit is a word with a broader meaning than make hay:

Other hypernyms of make hay include work.

make hay (noun)	exploit (noun)
	a notable achievement

make hay (verb)	exploit (verb)
turn to one's advantage	use or manipulate to one's advantage
	draw from; make good use of
	work excessively hard