deerhound vs hound dog

deerhound and hound dog both are nouns.

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

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

deerhound: very large and tall rough-coated dog bred for hunting deer; known as the royal dog of Scotland
hound dog: any of several breeds of dog used for hunting typically having large drooping ears

Other hypernyms of deerhound include hound.

deerhound (noun)	hound dog (noun)
very large and tall rough-coated dog bred for hunting deer; known as the royal dog of Scotland	any of several breeds of dog used for hunting typically having large drooping ears