North American or South American.

But usually they say where they are from in terms of their country. A Japanese person and a Russian, for example, don’t call themselves Asian. They would say they are Russian or Japanese.

In the case of the Americas someone would identify as Chilean, or perhaps Colombian. If you’re from Canada you’d say Canadian, and if you’re from the United States of America you’d say American because any other alternative sounds really dumb and nobody is going to use it.

If you’re from Europe do you call yourself Eurasian? Or are you French? Or British?

We really need to stop trying to make a big deal out of this “American” thing, or else I’m going to call everyone Africa-Eurasians, Americans, or Australians.

Also American.

Also North America and South America are generally considered two continents, and collectively referred to as The Americas. They have their own, unambiguous demonyms, North American and South American.

North Americans?

North American typically implies someone from the anglophone part of the continent.

Mexico is part of North America, and Mexico was included as part of the North American Free Trade Agreement (NAFTA) when it was active (reference: https://www.investopedia.com/terms/n/nafta.asp).

North American isn't typically used to refer to people at all. But in geopolitical contexts, it definitely refers to the entire continent (e.g. NAFTA)

No. Mexico is also included.