There'll probably soon be confused replies to this comment from Europeans: "But that is a football field!"
As to why we have two games,
(a) A game where you occasionally kick the ball, but mostly you toss the ball and carry it around,
(b) A game where you occasionally hit the ball with your head, knee or chest, but mostly kick the ball around, and touching the ball with your hands is not allowed,
Why (a) is called "football," and (b) is not, I don't know. Historical accident, maybe?
Sports is definitely not my strong point. I would probably have been better at gym class if it'd been about things like the etymology of the word "football" and the history of the sport, but alas, these facts were lacking from my formal education and aren't important enough for me to Google.