doggy vs domestic dog

doggy and domestic dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
doggy	Yes	No	No	No
domestic dog	Yes	No	No	No

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

doggy: informal terms for dogs
domestic dog: a member of the genus Canis (probably descended from the common wolf) that has been domesticated by man since prehistoric times; occurs in many breeds

Other hypernyms of doggy include Canis familiaris, dog.

doggy (noun)	domestic dog (noun)
informal terms for dogs	a member of the genus Canis (probably descended from the common wolf) that has been domesticated by man since prehistoric times; occurs in many breeds