primate vs simian

primate and simian both are nouns.

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

As nouns, simian is a hyponym of primate; that is, simian 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
simian: an ape or monkey

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

primate (noun)	simian (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	an ape or monkey
a senior clergyman and dignitary

primate (adjective)	simian (adjective)
	relating to or resembling an ape