Difference Between a water wheel and a water turbine?

[Physicist3]

Is the difference between a water wheel and a water turbine the fact that a water wheel is used to power a mechanical system where as a water turbine is connected to a generator to produce electricity? I understand that you can get undershot and overshot water wheels but do these also apply to water turbines?

 

[Simon Bridge]

A turbine is physically a different beastie to a wheel.
Google for the images and look.

Turbines are usually immersed - but don't have to be. If they are not immersed, then you can have the water pass over or under the hub.

Either can be used to make electricity or drive some other mechanical contrivance.
Either can be driven to push water as in a pump or a boat.