Although the etomology of the word football is inconclusive, the most likely explanation is that it’s a game played on foot, rather than on a horse.

Also, they’re both called football colloquially because they are both derived from a sport called Football but neither of them are actually “Football.” Association Football (Soccer) and Gridiron/American Football are the correct names. So really, people calling it Soccer are more correct than people who call it Football.