hearing dog vs working dog

hearing dog and working dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
hearing dog	Yes	No	No	No
working dog	Yes	No	No	No

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

hearing dog: dog trained to assist the deaf by signaling the occurrence of certain sounds
working dog: any of several breeds of usually large powerful dogs bred to work as draft animals and guard and guide dogs

hearing dog (noun)	working dog (noun)
dog trained to assist the deaf by signaling the occurrence of certain sounds	any of several breeds of usually large powerful dogs bred to work as draft animals and guard and guide dogs