primate vs hominid

primate and hominid both are nouns.

Word	Noun	Adjective	Verb	Adverb
primate	Yes	No	No	No
hominid	Yes	Yes	No	No

As nouns, hominid is a hyponym of primate; that is, hominid is a word with a more specific, narrower meaning than primate:

primate: any placental mammal of the order Primates; has good eyesight and flexible hands and feet
hominid: a primate of the family Hominidae

Other hyponyms of primate include simian, ape, anthropoid, hominoid, monkey, prosimian, lemur, tarsier.

primate (noun)	hominid (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	a primate of the family Hominidae
a senior clergyman and dignitary

primate (adjective)	hominid (adjective)
	characterizing the family Hominidae, which includes Homo sapiens as well as extinct species of manlike creatures