What's the difference between a potentiometer and a rheostat?
The correct term for the common terminal of a potentiometer is the slider.

A rheostat is simply a variable resistance used to control power to a load and you are correct about the wiring. Only the slider and one other terminal are used.

A potentiometer uses all three terminals, enabling a variable voltage or signal to be tapped off from the slider.

Potentiometers and rheostats are made the same way, but rheostats are usually much "beefier", as they are generally used in high-power situations.

The slider is often connected to one or other terminal for safety reasons, in case it loses contact with the track.