As for the history...
The Rugby Rules and the Sheffield Rules date from the 1850s
Ivy League teams started playing each other using a hybrid rule set in the 1860s, then more closely resembling Rugby in the 1870s
1872 The first meeting of the Football Association meets in London where they adopt the Sheffield Rules for Football, creating Association Football. The members who supported the Rugby Rules quit and form the Rugby Football Union.
1880-1890s Down and dstance rules, the forward pass and scrimmages are introduced into the collegiate game in the US by legends like Walter Camp, Pop Warner and John Heisman.
So... American Football is slightly younger than Association Football. But there's not a lot in it.