We have to thank the students of the 1880s for the word "soccer". It seems it was the practice amonst the well bred students of Oxford to abbreviate words whilst adding "er" to the end; "brekkers" for breakfast for example. One asked if he wanted to play "rugger" (i.e. the "rugby rules") a student replied "no, soccer", an abbreviation of "association", or the "association rules", i.e. the rules of the Football Association in London. As'soc'iation! "Footer" was also used, which is where the term football came from and is now widely used in the UK. (alot of people see the word 'soccer' as american, when really it was used before 'football') As for American Football, i'm not quite sure. It is played with the foot as well as the hands.... maybe 'handball' was already taken?!

Simply enough, all of these games are called "football", or were to begin with. Over the course of time, different rule specifications effectively made them different sports. So, different types of football became soccer (association football rules), rugby (rugby football rules) etc. The American game was more or less derived from rugby, and there are small similarities with the variety of rugby known as Rugby League, most notably the concept of a certain number of completed tackles (downs) to advance the ball, after which possession is turned over if no score results. The kicking element was originally much more common in the American game, with the concept of kicked goals from open play similar to dropped goals in rugby. The development of the forward pass pushed the kicking game to one side, as a thrown ball can be controlled much more accurately than a kicked one, and possession more safely retained. As for the name, in common with most varieties, it's just known as football to its own players, and American football to those who wish to distinguish it from other forms. In Ireland, the word football is generally used to refer to Gaelic football, an indigenous game with similarities to both soccer and rugby (round ball, but handling allowed). Similarly, Australian football (known sometimes as Australian Rules football) is simply referred to as football or footy in Australia. In England, football refers to soccer, unless otherwise specified.

'Soccer' can not have been used before 'football', as otherwise the Football As'soc'iation would not have been named so. I will concur, though, that 'soccer' was used in Britain before the US. Maybe I wasn't eloquent: the word 'association' was certainly not named after the sport, but before the sport, from French meaning congregate or join together. Association Football was so-called because of the association of teams which wanted to play against each other with the same rules. Soccer took it's name from Association Football. Therefore, 'soccer' must have been used after the word 'football'.