pooch vs domestic dog

pooch and domestic dog both are nouns.

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

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

pooch: 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 pooch include Canis familiaris, dog.

pooch (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

pooch (verb)	domestic dog (verb)
round one's lips as if intending to kiss