domestic dog vs pooch

domestic dog and pooch both are nouns.

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

As nouns, pooch is a hyponym of domestic dog; that is, pooch is a word with a more specific, narrower meaning than domestic dog:

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
pooch: informal terms for dogs

domestic dog (noun)	pooch (noun)
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	informal terms for dogs

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