I beg to differ, the story I heard goes back the late 19th century at Oxford/Cambridge Universities and was a bastardisation of the word 'Association'
FIFA-The Fédération Internationale de Football Association (English: International Federation of Association Football), UEFA-The Union of European Football Associations, FA-The Football Association. None of the governing bodies have the word soccer in the title
No, but what about the "Rugby Football Union" and all the other codes of Football throughout the World? All football, just a different kind. Its just a means of distinguishing them from each other.