America initially referred to what is now called "South America," and was later applied to what is now called "North America, as well as "Central America" and the Caribbean.
That includes Mexico and Canada and the United States of America.
Technically, there is no country called "America," but there is a federation of 50 countries who are located in North America, and people have taken to referring to it as "America" even though it is only part of an entire hemisphere that is the Americas.