Primates vs animal order

Primates and animal order both are nouns.

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

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

Primates: an animal order including lemurs and tarsiers and monkeys and apes and human beings
animal order: the order of animals

Primates (noun)	animal order (noun)
an animal order including lemurs and tarsiers and monkeys and apes and human beings	the order of animals