There is a super-continent known as the Americas or the New World. It is divided into two sections, North America and South America. In North America there are at least 23 officially recognized independent states or countries. To the far north is the state or country of Canada. Then there is a conglomeration of states comprising of the county The United States. Both those countries are of America. Below that is Mexico and assortment of other American countries such as Nicaragua, Panama, Belize, Cuba, Honduras, Jamaica and many more. They are all part of America and they had teams at the Olympics representing their state in the Americas. They are all American teams. So "America" isn't just the United States, it is a whole super-continent.
To further complicate things for our anchor who wasn't paying attention in class, there are a couple dozen independent territories owned by countries or states from the European continent such as the Cayman Islands (UK), Martinique (France), Aruba (Netherlands), Greenland (Denmark) and many more. So, does that mean France is part of America? I don't know. Maybe a news anchor will be able to tell us.