The wire itself is the same and carries the same number of amperes, but there are rules when you can use white versus black.
When using premade cables, sometimes the white wire is needed when connecting up a switch. A neutral is never connected to a switch terminal so a white wire on a switch terminal is not neutral. In that case the switched power (to the light, etc) goes on the black wire.
To connect 3 way switches, 3 conductor cable (14-3 on 15 amp circuits) is needed and preferably run directly from one switch to the other switch. Here use red and white for the travelers.
Put a band of red or black tape or stain on each end of a white wire connected to a switch.
For wires strung individually (through conduit) white is for neutral only.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.