Football (our football) and soccer (your football) are two entirely different sports. I believe it was called football because the ball is easier to send into the stratosphere with a kick than the traditional sphere.
Iirc, American football (
your football) and football (
our football) came about the same time.
Originally football was "association football", hence where the 'soccer' comes from.
I forget more than that. As with almost everything connected to both sports, the history really is tedious.