In American English (and I’m pretty sure British English too), America generally means the USA. And we don’t consider North and South America to be a single continent. If you want to refer to both you should say the Americas.
If you use the world America without other context, the lister will assume you are talking about the country and won’t even consider you mean North and South America combined.
I know some cultures consider the Americas to be a single continent. But that’s odd. They are arguably less combined than Europe, Asia, and Africa are.
