"Both the 'New York game' and the now-defunct 'Massachusetts game' versions of baseball, as well as softball, share the same historical roots as rounders"
WikipediaRounders is a bat-and-ball game played between two teams. Rounders is a striking and fielding team game that involves hitting a small, hard, leather-cased ball with a rounded end wooden, plastic, or metal bat. The players score by running around the four bases on the field.Played in England since Tudor times, it is referenced in 1744 in the children's book A Little Pretty Pocket-Book where it was called Base-Ball. The game is popular among British and Irish school children, particularly among girls. As of 2015 it is played by seven million children in the UK.Gameplay centres on a number of innings, in which teams alternate at batting and fielding. Points (known as 'rounders') are scored by the batting team when one of their players completes a circuit past four bases without being put 'out'. The batter must strike at a good ball and attempt to run a rounder in an anti-clockwise direction around the first, second, and third base and home to the fourth, though they may stay at any of the first three. A batter is out if the ball is caught; if the base to which they are running to is touched with the ball; or if, while running...
https://en.wikipedia.org/wiki/Rounders[https://en.m.wikipedia.org/wiki/Rounders]
I'm sure there were various early colonial and early American versions of similar games being played that really mushed up distinctions between British and American bat and ball Games. Interesting stuff.
....now I'm still trying to chase down more specificity on the origins of the word "soccer". I think the earliest known written reference is still in a letter written by the author of the poem with the well-known phrase "Days of Wine and Roses", in 1889.
"According to the Oxford English Dictionary, Dowson provides the earliest use of the word soccer in written language (although he spells it socca, presumably because it did not yet have a standard written form)."