game bird vs gallinaceous bird

game bird and gallinaceous bird both are nouns.

Word	Noun	Adjective	Verb	Adverb
game bird	Yes	No	No	No
gallinaceous bird	Yes	No	No	No

As nouns, gallinaceous bird is a hypernym of game bird; that is, gallinaceous bird is a word with a broader meaning than game bird:

game bird: any bird (as grouse or pheasant) that is hunted for sport
gallinaceous bird: heavy-bodied largely ground-feeding domestic or game birds

Other hypernyms of game bird include gallinacean, game.

game bird (noun)	gallinaceous bird (noun)
any bird (as grouse or pheasant) that is hunted for sport	heavy-bodied largely ground-feeding domestic or game birds