Overshot (and side-shot) wheels are generally the equivalent of pressure turbines.  They gently accept water at a high level ("high pressure" if it were put into a pipe and the pressure measured at the lower level), lower it like an elevator to a lower level, and gently release it.  In the process they recover nearly all of the energy represented by the mass times the change in gravitational potential.  (They CAN recover some energy from the momentum of the incoming water, but usually that's not much and that's not what they're optimized to grab.)

The height of an overshot wheel is the height of the "elevator", the height of the incoming water, and the height of the head.  If you can double the height of the wheel (without turning it into a side-shot) you were wasting half the head - and now you're not wasting it so you double your power.  If you turned it into a side-shot because it was already as high as the incoming water you didn't gain squat.

Undershot wheels are generally the equivalent of velocity turbines.  The accept water at a low level with a high velocity and slow it down, releasing it at an only slightly lower level (or even a HIGHER level if they've caused a "hydraulic jump", though the raceway is usually designed to avoid that) and a lower velocity.  They get their power from slowing the water.