hunting dog vs terrier

hunting dog and terrier both are nouns.

Word	Noun	Adjective	Verb	Adverb
hunting dog	Yes	No	No	No
terrier	Yes	No	No	No

As nouns, terrier is a hyponym of hunting dog; that is, terrier is a word with a more specific, narrower meaning than hunting dog:

hunting dog: a dog used in hunting game
terrier: any of several usually small short-bodied breeds originally trained to hunt animals living underground

hunting dog (noun)	terrier (noun)
a dog used in hunting game	any of several usually small short-bodied breeds originally trained to hunt animals living underground