titi monkey vs New World monkey

titi monkey and New World monkey both are nouns.

Word	Noun	Adjective	Verb	Adverb
titi monkey	Yes	No	No	No
New World monkey	Yes	No	No	No

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

titi monkey: small South American monkeys with long beautiful fur and long nonprehensile tail
New World monkey: hairy-faced arboreal monkeys having widely separated nostrils and long usually prehensile tails

Other hypernyms of titi monkey include platyrrhine, platyrrhinian.

titi monkey (noun)	New World monkey (noun)
small South American monkeys with long beautiful fur and long nonprehensile tail	hairy-faced arboreal monkeys having widely separated nostrils and long usually prehensile tails