Something is very strange here.

The replacement motor for this unit comes up as a DC motor.
That is why it has 4 wires.

The motor you describe sounds like an AC motor.
2 wires and they are the same color as it does not matter which wire goes to Neutral or power.

The motors are not interchangeable.

There have been problems with the DC motors re: very noisy, if the go they also blow the control board, etc.
In other words they are a pain in the you know what.

It sounds like someone has modified the unit to use an AC motor.

If you are happy with the units performance then I would get the numbers off the motor and use them to find a replacement.

It would be a good idea to check that you are getting 120 volts at the motor when the compressor is running.