A 'force' comes from when a runner is on 1st, and the batter puts the ball in play, the runner on 1st no longer has a right to the bag, that right now belongs to the batter. If he stays standing on 1st, he can still be tagged out. By convention, he can be 'outed' by touching the only base he now has a right to: 2nd. This is a 'force' out: he no longer has a right to any base, so he is now out. On a fly ball, the batter is out when the ball is caught, so the runner now has a right to either 1st or 2nd. By a separate rule, the runner is not allowed to advance from the base he has a right to (1st in this case) on a caught ball until after the ball is touched. The penalty of this rule, if successfully appealed, is that he is ruled out. He's not 'forced' to run back to 1st. He can keep running, and if no appeal is made he is safe. 'Forced', in the baseball sense, means he is forced off the base he was previously occupying, and his right to the next base removed by the defense, 'forcing' him out.
It's two entirely different types of outs. Baseball just chose to initiate the appeal by throwing to the previous bag. They could have chosen to do it by throwing to the mound, or the dugout, or whatever.
Or thought another way: the first play on the batted ball must be completed before the runner can score. If the runner is out before reaching first, then the inning ends exactly when the first play ends, so no run can score. On a fly ball, the first play ends when it is caught, because the batter is out. The attempt to double up the runner is a subsequent play. Don't be confused by both outs occuring from tagging the base, that's just a coincidence.