Help me with another question
 

This is hard for me to explain but I will try. The bases are loaded and the wrong batter comes to bat. They only have one out. They skip one guy. He hits the ball to the outfield. The runner at second base goes to home base but is out after the runner at third base goes to home base. The hitter runs all the way to second and the runner on first base stops at third base. The coach of the fielding team comes out and questions the umpire about the wrong guy hitting. Does the score count?

Speaking ASA (and it does make a difference)

Assuming the BOO is appealed properly, the batter which was due up is out. Any outs made during the play when the improper batter put the ball into play remain. And all other runners return to the base occupied at the TOP.

So, you now have three outs, runners left at the corners, no runs score and the player whose name follows that of the batter declared out leads off the inning. That is assuming that is not a player which was retired during the play in question. In your scenario, the improper batter from the previous inning is the lead off.

I think if not ASA, the outs made during the play do not remain, but all runners return to TOP. Someone please correct me if that is not the mentioned "it does make a difference".

In Fed the batters at bat I believe is negated.

In ASA you can get an out from said batter hitting say a flyball out.

So 2 outs on a play that in Fed gets you one out....

Actually in NFHS the outs made during the play count. 7.1.2 penalty (2). But there are rule sets that do not count outs made during the play.

I would agree that outs made during the play count, but not the improper batters. 7.1.2 penalty definetly states the improper batters time at bat is negated.