primate vs hominoid

primate and hominoid both are nouns.

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

As nouns, hominoid is a hyponym of primate; that is, hominoid 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
hominoid: a primate of the superfamily Hominoidea

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

primate (noun)	hominoid (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	a primate of the superfamily Hominoidea
a senior clergyman and dignitary