"Pool" as in a body of water is distinctive from the game of pool, which derives from French 'poule' which means "stakes" but also "hen".
What we think happened:
A game in the Middle Ages, 'jeu de la poule' ("chicken game") involved winning a chicken by hitting it with a small object.
So the "poule" was the chicken you were trying to win, which became the prototype for betting games.
How it came to be associated with the table sport is a little less clear, but may have simply been billiards played for money, with new rules to favor a clear winner.
