gay vs gay man

gay and gay man both are nouns.

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

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

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

gay (adjective)	gay man (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