gay woman vs homo

gay woman and homo both are nouns.

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

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

Other hypernyms of gay woman include gay, homophile, homosexual, adult female, woman.

gay woman (noun)	homo (noun)
a female homosexual	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