Reminds me of when I got into an argument with my English teacher in highschool. On a test we had to translate some words from Dutch to English, and she marked me down because I translated "aap" as "ape" intead of "monkey". I had to remind her that the movie "Planet of the Apes" exists.
Hey, you better take this meme and throw it in the fucking trash. Harambe was a gentle and kind soul. Gorilla was his final incarnation and his soul now rests in nirvana.
Cladistically apes are old world monkeys, as a branch of Simiiformes/Simians.
In casual conversation and scientific tradition, most people prefer to maintain a distinction between the two groups because they're referring to family characteristics and, in the greater social subtext, human ancestry. There is no actual scientific basis for excluding apes from the label of monkey beyond humanity's desire to feel special and to make evolution deniers feel dumb.
That said, that's a valid reason to continue using the distinction. If they try to argue the point just point out that they're admitting to the existence of evolution in doing so.
Tl;Dr all apes are now considered monkeys, but not all monkeys are apes