A potentiometer, like a rheostat, is a variable resistor. A rheostat has two terminals and a potentiometer has three. Wiring up a rheostat is easy--connect one wire to each terminal. As you turn the knob, the resistance to the flow of electricity through the rheostat changes. The three connections of the potentiometer opens up more possibilities. The path through the two outer connections goes through the whole potentiometer and turning the knob changes nothing. The centre connection is to the "wiper" that slides along the resistive element. A path that includes the wiper changes resistance as the knob is turned.
Connect a potentiometer to control current by connecting the central terminal to one of the outer terminals. Now the potentiometer acts like a rheostat--connect a wire to each outer terminal and the resistance along the connection changes as the knob is turned. This will only be true if it is a linear tapered potentiometer--all rheostats are linear tapered. Linear tapering just means that the resistance has a linear relationship with the angle that the knob is turned. Turning the knob half as far causes the potentiometer to have half the resistance.
Connect a potentiometer to control voltage by connecting the outer terminals to a power source and connecting the central terminal to act as a voltage divider. The outer connectors are connected across the output of one stage and the wiper, and one of the terminals forms the input to the next stage. This means that turning the knob divides up the voltage that is coming out the previous stage. At one end of the range, all of the voltage is being passed along, and at the other end of the range none of the voltage is being passed along. The voltage and current ways of using a potentiometer or both needed because some devices (further along in the circuit) are current driven and some are voltage driven.
Connect a linear potentiometer to control either current or voltage. The terminals, however, will not be in a row. Linear taper potentiometers (a.k.a. sliders or faders) have the outer connections at each end of the slider and the wiper connection will be on the other side. Faders are often used to mix tracks on sound recordings.
You do not really have to wire the wiper to one of the outer terminals to get a current controlling potentiometer; you can connect one wire to the wiper and the other to either terminal.
Since potentiometers are often used as volume controls the tapering is often non-linear (a.k.a. logarithmic) so the angle vs. resistance is flatter in the middle of the range. This makes the volume control more sensitive in the mid range of the volume. If you use a potentiometer that is not linear taper the resistance will not be proportional to the knob angle.