In the US, your home's power comes from a transformer that is center-tapped; the center tap is grounded typically both at the pole and at one location in your circuit breaker panel. The two legs of the transformer have 220/240 VAC on them. It is these two lines that are run to the pump. In addition, these lines are also typically run to power-hungry devices like the dryer, air conditioning, water heater, stove, etc.
See the attached schematic. The picture of the power pole is typical, although many neighborhoods now put these in power boxes to eliminate the poles. The 220/240 VAC is gotten from terminals A and C. Note the grounding of the neutral B -- it's connected to the grounded high voltage side and, through a 12 gauge bare wire to a ground buried in the earth when the power pole was installed. The 7200 VAC primary power is referenced to Earth ground (which should be obvious from the schematic).
Thus, to run any 220/240 VAC device, the device's terminals are connected to terminals A and C to make up the circuit. There is no neutral involved at all. It would have been better for the neutral to have been called the center tap, but unfortunately the nomenclature is pretty well fixed.
Note that the voltage between terminals A and B is 120 VAC, as it also is for the terminals B and C. These two terminals are used for the 120 VAC branch circuits in your house; you can see that a neutral connection is always involved and that the neutral is always near ground potential.
Typically, the three wires going to your pump are a grounded wire and these two 240 VAC power lines.