the 2 hots are easy.. they carry the 240 volt currents

now it gets a little more complicated
the neutral..this wire carry current for 120 volt circutis
even a dryer has 120 volt circuits..and currents..so some current flow on the neutral wire..yes even in a 240v dryer..the mechanical timer..most likely is 120v..

the ground...you know the wire that ties to the neutral at the panel?
this wire..well it doesn't carry current unless there is a fault..hence its a safety ground..

got it?
the center tap of the transformer is tied to earth ground as a safety measure..a local ground reference..a place for fault currents to flow..

dryers and rangs ad a special exception that allowed -wire ciruits.

Sonce the timers and often the drum morot are often 120 V loads the dryer was really a 120/240 V combination load that would require a 4-wire circuit.

The exception allowed 9and still grandfathers) 3-wire circuits for ONLY dryers and ranges.

All other 120/240 V loads have required 4-wres for a very long time.

The circuit used to power houses and large residential loads is an Edison circuit.

It has the advantage of having 240 V available for larger loads, while not having any voltage greater than 120 V to ground (or neutral) present.

There is ALWAYS a voltage drop in a wire carrying current, no matter how large the wire is.

The grounding conductor (AKA 'safety ground') is NOT intended to be part of the circuit in normal operation.

It is there to keep the chassis at zero volts to earth, and provide a path for fault currents to trip breakers (or fuses) if the chassis should become electrically hot from a fault in the equipment.
If the ground was not present the chassis could be at 120 V until another path to ground occurs, like through a person touching the chassis and a ground.

Very old radios without a polarized plug could have the chassis at 120 V.
Touch a metal knob or the chassis and ground and you competed the circuit.

Since no current is flowing in the grounding conductor (safety ground) it is reliably at zero volts to earth.

The neutral (AKA grounded conductor) is NOT at zero volts since it is part of the circuit, carries current, and the current creates a voltage drop (it may be very small, but it is not zero).

A typical US house uses an Edison circuit, created by grounding the center tap of the secondary winding on the pole transformer.

This limits the voltages to 120 V to earth, while providing 240 V leg-to-leg for larger loads.
Since transformers always have leakage from the primary side to the secondary side (through inter-winding capacitance) and the lowest distribution voltage is 7,200 volts the secondary will charge to this value if it is not connected to the primary somehow to create a return path for the leakage current.
This is normally done by using a 3-phase Y to distribute power, with the center of the Y connected to earth and used as a neutral to return any imbalance in the three phase loads.
One side of each phase transformer is thus tied to earth and neutral.
Any leakage from the primary side can then return through the earth connection from the house main panel to the pole primary earth connection.
While the earth is a poor conductor at 120 V, it works well at 7,200 V (and higher) most of the time.
In some areas (sandy dry soil) a neutral is run on the poles to ensure it is available for current even when the earth resistance is excessive.

One of the hazards that was created by using metal water pipes as a grounding electrode is that water line workers can be injured or killed.
If they cut a water line and then touch each side of the cut pipe there can be enough voltage and current to kill.

Arguably the current might still be there if the pipe was NOT used as a grounding electrode though.
The pipe would likely still be a lower impedance path, and current would preferentially flow in it over a higher impedance earth only path.