There is no difference in pump performance with either voltage. There are advantages of using the higher voltage since the pump will not pull as many amps when using 230VAC. Lower amperage may also allow you to use a smaller wire size to supply power to the pump.
Click here to see a diagram on how to wire a pump start relay.
The difference between a 2-wire and 3-wire pump is based on the type of motor that is used. A 3-wire single-phase motor requires a control box with a starting capacitor. Because of this starting arrangement, the motor requires three “hot” leads (plus a lead for the ground connection) to operate correctly. It is called a “3-wire” due to the three “hot” leads, though there are actually four wires when you count the ground wire. The 2-wire motor requires no control box because is does not use a starting capacitor. Instead, a 2-wire motor has a built-in electrical device that is used to get the motor started. This only requires the pump to have two “hot” leads (plus ground), which is why it is called a “2-wire” pump. The confusion sets in when counting the total number of wires as a 2-wire pump actually has three wires and a 3-wire pump has four wires.