In Star Trek there is a fictional interplanetary federal republic called The United Federation of Planets and it is referred to as The Federation (do you see the analogy?).
Under the wrong argument it should be called The Planets, which it is plain non-sense. Following this example it is quite easy to deduce that The United States of America should (if needed) be referred as The States but never as America.
Please, note that this page in not about demonyms (gentilics) but about the way to call a country.
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Let the world know that USA should not be called America! America is one whole continent.