Here's a silly video explaining the Backward Compatiblity feature.
As far as the controller remapping goes, it's not as simple as Backward compatibility.
"Before getting too excited, though, know that this isn't as extensive as what's possible with the Elite controller. As explained by Microsoft's Major Nelson, button remapping with a standard controller amounts to swapping button assignments.
If you want the Y button to serve as the X button, the X button will then automatically begin to serve as the Y button. You're free to continue swapping assignments, but there's no way to remove an input from the controller or have multiple buttons all do the same thing (both of which are possible with an Elite). Still, as laborious as the setup process sounds, it's certainly preferable to being unable to reassign buttons at all."
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