order Cetacea vs animal order

order Cetacea and animal order both are nouns.

Word	Noun	Adjective	Verb	Adverb
order Cetacea	Yes	No	No	No
animal order	Yes	No	No	No

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

order Cetacea: an order of Eutheria, containing the whales, dolphins, and porpoises (Cetacea)
animal order: the order of animals

order Cetacea (noun)	animal order (noun)
an order of Eutheria, containing the whales, dolphins, and porpoises (Cetacea)	the order of animals