domesticated animal vs fauna

domesticated animal and fauna both are nouns.

Word	Noun	Adjective	Verb	Adverb
domesticated animal	Yes	No	No	No
fauna	Yes	No	No	No

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

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

Other hypernyms of domesticated animal include animal, animate being, beast, brute, creature.

domesticated animal (noun)	fauna (noun)
any of various animals that have been tamed and made fit for a human environment	a living organism characterized by voluntary movement
	all the animal life in a particular region or period