What a making results in, offered to others. Named from the side of what comes out rather than what went in.
Latin productum (something produced), from producere (to lead forward, to bring forth): pro- (forward) + ducere (to lead); a product is named from the leading-out rather than from the leading-in.
What a making results in, once it is offered to others. The root's direction matters: a product is named for what came out the far end, not for the labour that went into it.