game fowl vs domestic fowl

game fowl and domestic fowl both are nouns.

Word	Noun	Adjective	Verb	Adverb
game fowl	Yes	No	No	No
domestic fowl	Yes	No	No	No

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

game fowl: any of several breeds reared for cockfighting
domestic fowl: a domesticated gallinaceous bird thought to be descended from the red jungle fowl

Other hypernyms of game fowl include fowl, poultry.

game fowl (noun)	domestic fowl (noun)
any of several breeds reared for cockfighting	a domesticated gallinaceous bird thought to be descended from the red jungle fowl