From a linguistics perspective, United States refers to the whole of the Americas, as they are the "United States" of the American continents. Technically speaking though it is rare for a denonym to refer to the political part of a nation's name (Russian Federation, United States of America, Union of Soviet Socialist Republics , Peoples Republic of China.
Thus either way any denonym deriving from the term "United States of America" is incorrect, unless we include the whole name; United States of American.
But who cares? American is fine. It may not be technically correct but it is what the majority of the people in the country refer to themselves as.






