EF-S lenses have the rear lens closer to the sensor on a crop camera.
I think that is incorrect. Both Canon APS-C and Canon FF EOS cameras have identical register distance.
Actually it is correct. Yes, APS-C, APS-H, and FullFrame cameras all share the same 44mm "Register" or "Flange Mount Distance", but EF-S lenses DO have the rear element positioned closer to the sensor. This theoretically allows for a smaller lens design to cover a smaller sensor. It also requires a smaller mirror so that it does not hit the rear element.