I imagine most people realise that the word "Soccer" isn't an American coinage, it's the normal abbreviation for "Association Football" - as opposed to all the other football codes, such as Rugby Football (in either of its two versions), or Gaelic Football, or Australian Rules, or American Football.

Basically "Football" is what people call whatever happens to be the most popular version in their country. In most parts of Ireland "Football" tended to mean Gaelic Football , but these days it's changed. When Soccer becomes the main type of football in the USA, I imagine it'll be called Football. Or maybe Fútbol.