primate vs lemur

primate and lemur both are nouns.

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

As nouns, lemur is a hyponym of primate; that is, lemur 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
lemur: large-eyed arboreal prosimian having foxy faces and long furry tails

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

primate (noun)	lemur (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	large-eyed arboreal prosimian having foxy faces and long furry tails
a senior clergyman and dignitary