A single unit run capacitor is generally used in smaller air conditioner units. A single unit run capacitor will have two connections and will be hooked up to a single motor.
A dual run capacitor is essentially just two run capacitors in one. They have nothing else that makes them electrically special. A dual run capacitor supports two electric motors, such as in large air conditioner or heat pump units, with both a fan motor and a compressor motor.
A dual run capacitor will generally have three connections:
"H" or "Herm" for "Hermetic Compressor"
"F" for "Fan"
"C" for "common"
They will also have two different ratings for the two different run capacitors. For example, you might see 40/5 MFD, meaning that one side is 40 microfarads (measurement of capacitance), and the other side is 5 microfarads. The smaller value will always be connected to the fan, while the larger connection will always be connected to the compressor.
If necessary, you can use two separate run capacitors in place of your original dual run motor capacitor, as long as there is enough space for both.
You should be able to tell which type of run capacitor you need by how many connections your old one has.