Rugby is the link between soccer and football
Soccer features a round ball and 45 minute halves played continuously. Most of the world calls it football because it's played primarily using the feet.
American Football features an oblong, pointed ball, and is played in 6 second increments. How can a sport played primarily using the hands and arms be called football?
The answer is the sport that links them: Rugby.
If a school ball game in Rugby, England hadn't been modified one day in 1823, maybe people would have come to know that game as Rugby football. One boy at the school, William Webb Ellis, is reputed to have played the game differently: he picked up the ball and advanced it in his arms.
Fast forward a few decades, a few rule adjustments, add a ball that is a little more lemon-shaped, and Rugby Football, became very popular throughout all British-influenced societies. British colonialism guaranteed the popularity of rugby, even in America. In fact, rugby predates football as one of the oldest collegiate sports played in the States.
Just like those young English students changed a ball game into rugby, young American students changed rugby into football. In rugby, one must touch the ball down in the try-zone to be awarded points. The football equivalent of reaching the end zone is called a try. In rugby, play can be re-started from a scrum, the football equivalent of a restart of play begins at the line of scrimmage.
Rugby is the link between soccer and football, combining many aspects of both, and involving certain components of wrestling.