Variable resistor is used to carry the current while providing voltage drop.
i.e. on a dimmer switch, the more resistance it puts out, the darker the lights are.
Potentiometer is basically a Variable resistor, but it works as an input sensor which provides a signal. it does not carry the current goes to the load component.
i.e. the foot pedal on a Tig welder, it tells the welding power source how much amperage it needs to put out, but, welding current doesn't flow through the foot pedal itself.