Dead Ball or Out?

[AtlUmpSteve]

I believe we have all come to terms with the difference between a discarded bat hitting the ball in fair territory (dead ball, out), and the ball hitting a discarded bat in fair territory (play on, ball live, bat is now part of the field).

So why don't we get the (similar) difference between a batted ball hitting a batter that is still in the batter's box (dead ball, foul ball), and a batter-runner that makes contact with a fair batted ball (dead ball, out), whether in the box, partially in the box or (obviously) out of the box?

It seems so simple, why is it an issue? Same in every rule set, and actually the same as baseball.