They are at the same potential but with one very important distinction. The neutral wire carries the full load current as the hot wire while the ground carries absolutely zero current. The neutral is designed to be the return for the hot wire to complete the circuit.
Anything else is a fault condition. Safety equipment depends on this distinction. When current flows in the ground wire, there is a leakage path and properly designed equipment will shunt fault currents here rather than to the user.
The Neutral wiring in any circuit is the return path for the live or outgoing current. They work as a pair. The Ground is for safety, it is the protection wire, and its purpose is to make sure that any metal or conductive part that you could touch is safe, at the same potential as the ground that you stand on. Earth or Ground wires should never be conducting any current, unless there is an electrical fault, then it carries the Fault current safely to earth and hopefully trips the circuit breaker on the faulty circuit.
The three pins correspond to earth, neutral, and phase. The phase line is the one that carries the current, the neutral line provides the return path to balance the flow of current, and finally earthing is purely used for safety purposes.
In most electrical systems, there are three wires in plugs because they are used to connect the three primary components of the electrical system: the live wire, the neutral wire, and the ground wire.
The live wire carries the electric current from the power source to the load. It is usually colored black, red, or another color to indicate that it is live. The neutral wire carries the electric current back to the power source after it has passed through the load. It is usually colored white or gray.
The ground wire is a safety feature that is used to provide a path for electricity to flow in the event of a fault or short circuit. It is usually colored green, or it may have a green stripe to indicate its purpose.
The live and neutral wires are fundamentally different because they serve different purposes in the electrical system. The hot wire carries the electric current to the load, while the neutral wire carries it back to the power source. The ground wire is not involved in the flow of electric current under normal circumstances, but it serves as a safety feature by providing an alternative path for electricity to flow in the event of a fault.
Therefore, there are three wires in electricity plugs to connect the live wire, the neutral wire, and the ground wire, which are all necessary components of the electrical system.