@immatthewj
The neutral doesn’t carry voltage, it carries current. A voltage appears only when there is resistance to that current.
Look at the formula:
V = I (or A for amps) x R
In ideal neutral or ideal ground, R is zero, so V is zero. Lets imagine a circuit with a 5A load. Say an idling tube amplifier. The neutral and hot should be balanced, so the neutral wire has this voltage on it:
V = 5A x 0 = 0
Often we’ll see 2 to 4 or 5V on a decently wired neutral due to R not actually being exactly zero.
The problem is that there are lots of connections in a home and some are bound to come loose and increase the relative resistance.
Now lets see why N and G are different in the case of a bad conductor. Lets say instead of 0 resistance you have 10 Ohms on either the neutral or ground wire.
The ground wire carries no current normally, so if you were to touch the ground wire you experience:
V = 0A x 10R = 0V
The neutral on the other hand carries current, so with the same situation:
V = 5 x 10 = 50V
Now we have 50V, already a potentially lethal situation if one touches this with wet hands.

