staghound vs hound dog

staghound and hound dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
staghound	Yes	No	No	No
hound dog	Yes	No	No	No

As nouns, hound dog is a hypernym of staghound; that is, hound dog is a word with a broader meaning than staghound:

staghound: a large heavy hound formerly used in hunting stags and other large game; similar to but larger than a foxhound
hound dog: any of several breeds of dog used for hunting typically having large drooping ears

Other hypernyms of staghound include hound.

staghound (noun)	hound dog (noun)
a large heavy hound formerly used in hunting stags and other large game; similar to but larger than a foxhound	any of several breeds of dog used for hunting typically having large drooping ears