terrier vs hunting dog

terrier and hunting dog both are nouns.

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

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

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

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