A gathered quantity held in common and drawn from as needed. What is in it belongs to the pool, not to any one drawer.
French poule (a stake played for in a game, literally 'hen'), borrowed into English gambling slang by the 19th century for a common stake everyone contributes to and draws from — a separate root from the older Old English word for a body of still water, though the two now read as one word.
A gathered quantity held in common, contributed to and drawn from by more than one — what is in it belongs to the pool itself, not to whoever last drew from it.