Well, everybody born in the american continent is technically “american” too, including Central and South America. Is there a specific term in english for these people?
Edit: Thanks for all your answers, especially the wholesome ones and those patient enough to explain it thoroughly. Since we (South Americans) and you (North Americans) use different models/conventions of continent boundaries, it makes sense for you to go by “Americans”, while it doesn’t for us.
There is no continent called "America". We have North America and South America.
When someone says "South American" I don't think Alabama I think Brazil or Argentina.
The term "North American" is commonly used when you're describing something that applies to both Canada and the US. Eg. "North American sports teams".
We commonly use the term "Central American" when referring to Mexico, El Salvador, etc. because even though they are technically in North America there is a strong cultural divide, similar to how the middle East is technically Asia, but you'd never refer to someone from Saudi Arabia as "Asian".
Mexico is also in North America though, not in Central America.
LATAM are usually pissy about the term "Americans" because the "geographical division" colloquially seem to be more of a third vs. first world division rather than a geographical division.
You can see how people from LATAM usually call themselves "americanos" to include everyone from The Americas, but Canada and USA think "North America" doesn't include Mexico.
It's understandable for El Salvador, but México it's absolutely part of North America.