depilatory vs cosmetic

depilatory and cosmetic both are nouns.

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

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

depilatory (noun)	cosmetic (noun)
a cosmetic for temporary removal of undesired hair	a toiletry designed to beautify the body
a chemical (usually a sulfide) used to remove hair or wool or bristles from hides

depilatory (adjective)	cosmetic (adjective)
able to remove hair or render hairless	serving an aesthetic purpose in beautifying the body
	serving an esthetic rather than a useful purpose