adult vs woman

adult and woman both are nouns.

Word	Noun	Adjective	Verb	Adverb
adult	Yes	Yes	No	No
woman	Yes	No	No	No

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

adult (noun)	woman (noun)
any mature animal	women as a class
a fully developed person from maturity onward	an adult female person (as opposed to a man)
	a female person who plays a significant role (wife or mistress or girlfriend) in the life of a particular man

adult (adjective)	woman (adjective)
(of animals) fully developed
designed to arouse lust