Strictly speaking that should be association football, although everyone calls it football outside the US of course.
"Football" existed before, but simplifying somewhat, just about all the modern games of football derive from rules codified at British private-education schools in the 19th century. So for example, rugby football originated at Rugby private-education school, which then developed into American football. Off the top of my head I can think of association football, American football, Canadian football, rugby football, Australian rules football and Gaelic football.
