A resistor trimmer is a variable resistor that is designed to be infrequently adjusted, usually just at the point of manufacture or when the unit is being recalibrated.  They are placed along the circuit at critical points that need to carefully tuned for optimal functionality.  Usually, a small screw at the top of the resistor body makes the resistance adjustment.  The body itself is mounted directly onto the board.  Because they are calibrating devices, their resistive range is often very small, and very accurate settings can be achieved through adjustment.

Potentiometers and rheostats are often used interchangeably and can refer to the same device structures.  They are variable resistors constructed with a three terminal form.  Two of the terminals are attached to each end of the resistor, like a normal fixed resistor structure.  The third terminal is connected to a device called a slider.  This is a conductive wiping mechanism that can be swept across the resistor in a semi-continuous pattern and create a conductive pathway between the end terminals and the wiper terminal.  They can be designed to have a different resistive output depending on the location of the adjuster knob or slider.  Some are designed to have a linear output and others, especially in audio functions, have outputs resembling logarithmic scales.