Word association

football (n.)
open-air game, first recorded c.1400; see foot (n.) + ball (n.1). Forbidden in a Scottish statute of 1424. The first reference to the ball itself is late 15c. Figurative sense of “something idly kicked around” is first recorded 1530s. Ball-kicking games date back to the Roman legions, at least, but the sport seems to have risen to a national obsession in England, c.1630. Rules first regularized at Cambridge, 1848; soccer (q.v.) split off in 1863.

The U.S. style (known to some in England as “stop-start rugby with padding”) evolved gradually 19c.; the first true collegiate game is considered to have been played Nov. 6, 1869, between Princeton and Rutgers, at Rutgers, but the rules there were more like soccer. A rematch at Princeton Nov. 13, with the home team’s rules, was true U.S. football. The earliest recorded application of the word football to this is from 1881.

soccer (n.)
1889, socca, later socker (1891), soccer (1895), originally university slang (with jocular formation -er (3)), from a shortened form of Assoc., abbreviation of association in Football Association (as opposed to Rugby football); cf. rugger, but they hardly could have taken the first three letters of Assoc.