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