@JohnPhilpin I think you are right: American football is a fork of rugby only with an advertising infested flow added. As we do.
Soccer, well the British started out calling it soccer then changed it later to football. Americans already had American football and we must not dilute the branding so we went with the term soccer.
And I'm not going to be too hard on the USA for whatever we want to call soccer/football because getting a new (for us) sport established in the US in only one generation was a huge social undertaking. When I was in high school, most schools did not have even a soccer club let alone a team. Soccer was almost unheard of here. And now it's everywhere with huge grass roots support.