cosmetic vs makeup

cosmetic and makeup both are nouns.

Word	Noun	Adjective	Verb	Adverb
cosmetic	Yes	Yes	No	No
makeup	Yes	No	No	No

As nouns, makeup is a hyponym of cosmetic; that is, makeup is a word with a more specific, narrower meaning than cosmetic:

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

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