Does this actually cause any meaningful confusion?
In English there isn't a singular place called "America". As you mention, there's North/South/Cebtral, and together they're referred to as "the Americas". When someone refers simply "America" with no other qualifier, it's clear what they mean.
(Of course in Spanish "America" refers to the whole thing because North and South America aren't considered separate continents. But they have a different demonym for the US in Spanish)
In English there isn't a singular place called "America". As you mention, there's North/South/Cebtral, and together they're referred to as "the Americas". When someone refers simply "America" with no other qualifier, it's clear what they mean.
(Of course in Spanish "America" refers to the whole thing because North and South America aren't considered separate continents. But they have a different demonym for the US in Spanish)