gay man vs homo

gay man and homo both are nouns.

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

As nouns, homo is a hypernym of gay man; that is, homo is a word with a broader meaning than gay man:

Other hypernyms of gay man include gay, homophile, homosexual, adult male, man.

gay man (noun)	homo (noun)
a homosexual man	any living or extinct member of the family Hominidae characterized by superior intelligence, articulate speech, and erect carriage
	someone who is sexually attracted to persons of the same sex