primate vs ape

primate and ape both are nouns.

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

As nouns, ape is a hyponym of primate; that is, ape 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
ape: any of various primates with short tails or no tail at all

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

primate (noun)	ape (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	any of various primates with short tails or no tail at all
a senior clergyman and dignitary	person who resembles a nonhuman primate
	someone who copies the words or behavior of another

primate (verb)	ape (verb)
	represent in or produce a caricature of
	imitate uncritically and in every aspect