gay vs gay woman

gay and gay woman both are nouns.

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

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

gay (noun)	gay woman (noun)
someone who is sexually attracted to persons of the same sex	a female homosexual

gay (adjective)	gay woman (adjective)
bright and pleasant; promoting a feeling of cheer
brightly colored and showy
homosexual or arousing homosexual desires
given to social pleasures often including dissipation
offering fun and gaiety
full of or showing high-spirited merriment