primate vs eutherian

primate and eutherian both are nouns.

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

As nouns, eutherian is a hypernym of primate; that is, eutherian is a word with a broader meaning than primate:

primate: any placental mammal of the order Primates; has good eyesight and flexible hands and feet
eutherian: mammals having a placenta; all mammals except monotremes and marsupials

Other hypernyms of primate include eutherian mammal, placental, placental mammal.

primate (noun)	eutherian (noun)
any placental mammal of the order Primates; has good eyesight and flexible hands and feet	mammals having a placenta; all mammals except monotremes and marsupials
a senior clergyman and dignitary

primate (adjective)	eutherian (adjective)
	of or relating to or belonging to the subclass Eutheria