Lagomorpha vs animal order

Lagomorpha and animal order both are nouns.

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

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

Lagomorpha: rabbits, hares, pikas; formerly considered the suborder Duplicidentata of the order Rodentia
animal order: the order of animals

Lagomorpha (noun)	animal order (noun)
rabbits, hares, pikas; formerly considered the suborder Duplicidentata of the order Rodentia	the order of animals