domestic dog vs domestic animal

domestic dog and domestic animal both are nouns.

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

As nouns, domestic animal is a hypernym of domestic dog; that is, domestic animal is a word with a broader 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
domestic animal: any of various animals that have been tamed and made fit for a human environment

Other hypernyms of domestic dog include domesticated animal, canid, canine.

domestic dog (noun)	domestic animal (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	any of various animals that have been tamed and made fit for a human environment