make-up vs cosmetic

make-up and cosmetic both are nouns.

Word	Noun	Adjective	Verb	Adverb
make-up	Yes	No	No	No
cosmetic	Yes	Yes	No	No

As nouns, cosmetic is a hypernym of make-up; that is, cosmetic is a word with a broader meaning than make-up:

make-up (noun)	cosmetic (noun)
cosmetics applied to the face to improve or change your appearance	a toiletry designed to beautify the body
the way in which someone or something is composed
an event that is substituted for a previously cancelled event

make-up (adjective)	cosmetic (adjective)
	serving an aesthetic purpose in beautifying the body
	serving an esthetic rather than a useful purpose