The neutral wire in an electrical system does carry current but the current in a neutral wire is carried under no pressure and is just a return path for the electricity.
The hot wire carries the electricity under full pressure and is why you get a shock from it but the neutral wire carries the electricity back under no voltage pressure.
So that's why if you test for electricity on the neutral wire on an energized circuit there should be no voltage reading on the neutral wire but there will be on the hot wire.