This probably differs a bit between languages. In Dutch, we call both monkeys and apes "aap", and apes specifically "mensaap" (human-ape).

Relevance? I am sure Dutch zoologists would similarly agree that use of the term 'monkey' is just plain wrong in this instance.

Cladistically, apes are monkeys.

I think you mean primates?

No. Apes (including humans) are more closely related to old world monkeys than new world monkeys are. When you are more closely related to monkeys than other monkeys are, most people would say you are a monkey. Including me.