sausage dog vs badger dog

sausage dog and badger dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
sausage dog	Yes	No	No	No
badger dog	Yes	No	No	No

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

sausage dog: informal term
badger dog: small long-bodied short-legged German breed of dog having a short sleek coat and long drooping ears; suited for following game into burrows

Other hypernyms of sausage dog include dachshund, dachsie.

sausage dog (noun)	badger dog (noun)
informal term	small long-bodied short-legged German breed of dog having a short sleek coat and long drooping ears; suited for following game into burrows