Depends on language and culture and context. In the United States we use America to refer to the country and North America and South America to refer to the continents. Many Latin American countries use a six continent system though, where North America and South America are just one continent called America. This can lead to some tension and confusion when people from the United States call themselves American, since that would imply everyone in the western hemisphere bascially. While sometimes "Americano" is used to refer to people from the United States, you'll also you get descriptors like "estadounidense" in Spanish for this reason. Though this also has ambiguity, since technically Mexico is also a "united states."

Anyways, point is, a seven continent system with the western hemisphere separated into north and south America isn't used everywhere, for some people America is a continent. In some places Europe and Asia are combined, and there's other variations too. None of them like up with plate tectonics or anything perfectly, so they're all a little arbitrary in the end.

https://en.m.wikipedia.org/wiki/Continent