macaque vs Old World monkey

macaque and Old World monkey both are nouns.

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

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

macaque: short-tailed monkey of rocky regions of Asia and Africa
Old World monkey: of Africa or Arabia or Asia; having nonprehensile tails and nostrils close together

Other hypernyms of macaque include catarrhine.

macaque (noun)	Old World monkey (noun)
short-tailed monkey of rocky regions of Asia and Africa	of Africa or Arabia or Asia; having nonprehensile tails and nostrils close together