mangabey vs Old World monkey

mangabey and Old World monkey both are nouns.

Word	Noun	Adjective	Verb	Adverb
mangabey	Yes	No	No	No
Old World monkey	Yes	No	No	No

As nouns, Old World monkey is a hypernym of mangabey; that is, Old World monkey is a word with a broader meaning than mangabey:

mangabey: large agile arboreal monkey with long limbs and tail and white upper eyelids
Old World monkey: of Africa or Arabia or Asia; having nonprehensile tails and nostrils close together

Other hypernyms of mangabey include catarrhine.

mangabey (noun)	Old World monkey (noun)
large agile arboreal monkey with long limbs and tail and white upper eyelids	of Africa or Arabia or Asia; having nonprehensile tails and nostrils close together