The logic of it is simple to me. The name "America" was initially assigned to a newly discovered area in the south, and was later used for the entire land mass. Eventually the USA was founded in part of that area, but with such an unwieldy name, "America" became a popular abbreviation. That doesn't invalidate the original meaning. I understand that it's not ambiguous to many people, but it's ambiguous in my own mind because I do think of "America" as applying to the entire land mass.
It does invalidate the original meaning because no one uses America to refer to that landmass anymore (in English). Common use is what determines the meaning of language.
"Nice" used to mean simple or foolish, "Silly" used to mean blessed, and "Awful" used to mean worthy of awe--modern usage patterns have invalidated their original meanings in modern use.
>I understand that it's not ambiguous to many people, but it's ambiguous in my own mind because I do think of "America" as applying to the entire land mass.
And I think of Columbia as an alternate name for the US. It doesn't mean I'm going to get on a Colombian Spanish language forum and start making up new demonyms for them.