police dog vs working dog

police dog and working dog both are nouns.

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

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

police dog: any dog trained to assist police especially in tracking
working dog: any of several breeds of usually large powerful dogs bred to work as draft animals and guard and guide dogs

police dog (noun)	working dog (noun)
any dog trained to assist police especially in tracking	any of several breeds of usually large powerful dogs bred to work as draft animals and guard and guide dogs