Single phase electric motors use a device called a starting capacitor to create a large phase shift to produce necessary torque during start up. Single phase motors will commonly have both a run capacitor and a starting capacitor. Starting capacitors differ from run capacitors by their relative capacitance value being much higher for a given physical size. The starting capacitor will usually be identified as having a black phenolic or plastic case and a recessed top where the connections are located.
As a byproduct of high capacity, they are only intermittent rated and can only be energized for a few seconds at a time. For this reason, a starting capacitor is usually one of the first components to fail on single phase electric motors.
A motor run capacitor is engaged in a circuit all the time for phase delay or power factor correction. They are common in HVAC units and larger single phase motors. They are oil cooled, in metal cases, and have fairly low capacitance ratings (such as 5 uf or 45 uf). Run capacitors are usually rated for 370V or 440V.
If you're sizing a capacitor to start with (and not merely replacing an old one), make sure that your capacitor voltage rating is 1.5x your line rated voltage. This is because the voltage ratings on AC capacitors are not RMS, but rather, peak to peak voltage.
On 240V system, run capacitors are generally 370-440V, and in 480V systems, you'll often see 600V capacitors used. This is to account for the peak to peak voltage levels in the system.
Starting capacitors are usually physically bigger than run capacitors. They also tend to be larger in capacitance values (such as 430-516 uf). Their capacitance ratings come in a range instead of a set number, like in run capacitors. This is because the phase shift produced by running AC current through a start capacitor doesn't need to be as precise to get the motor turning during start up. Common voltage ratings for a starting capacitor are 110/125V, 165V, 220/250V, or 330V.