Potentiometers:
A potentiometer is a simple electromechanical transducer.  It converts rotary or linear motion from the operator into a change of resistance, and this change can be used to control anything from the volume of a hi-fi system to the flaps of an aeroplane.

Trimmers
Trimmers are designed for "set and forget" applications.  They are used for "trimming" the value of a resistor, and are used for calibrating instruments, setting the bias current on power amplifiers, and a host of other applications.

A normal panel potentiometer could do the same, but these are normally bigger and more expensive.