Real Dictionary

monkey
If you refer to a child as a monkey, you are saying in an affectionate way that he or she is very lively and naughty.
countable noun: A monkey is an animal with a long tail which lives in hot countries and climbs trees.

monkey in American English
any of several families of Old and New World primates usually having a flat, hairless face and a long tail
to play, fool, trifle, or meddle
noun: any mammal of the order Primates, including the guenons, macaques, langurs, and capuchins, but excluding humans, the anthropoid apes, and, usually, the tarsier and prosimians

monkey in British English
noun: any of numerous long-tailed primates excluding the prosimians (lemurs, tarsiers, etc): comprise the families Cercopithecidae (Old World monkeys), Cebidae (New World monkeys), and Callithricidae (marmosets)