AFAIK, when the game reached the US, the "version" of football that came over, was the type of football being favored at Rugby. At that time in the UK, the sport football was being played in two different versions. But it was "football" that came over to the US, not rugby, as it was not called "rugby" yet. In then evolved on its own and is now, as we know, very different from rugby, which is what it turned into in the UK.
Did that make any sense?