domestic animal vs creature

domestic animal and creature both are nouns.

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

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

domestic animal: any of various animals that have been tamed and made fit for a human environment
creature: a living organism characterized by voluntary movement

Other hypernyms of domestic animal include animal, animate being, beast, brute, fauna.

domestic animal (noun)	creature (noun)
any of various animals that have been tamed and made fit for a human environment	a living organism characterized by voluntary movement
	a living being
	a person who is controlled by others and is used to perform unpleasant or dishonest tasks for someone else