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Live supplies the electricity.

Neutral returns the electrical path to ground and is a grounded conductor. It completes the circuit.

The earth or "grounding conductor" is another grounded conductor that normally doesn't carry any significant current (except perhaps a small bit of leakage). It's there for safety so that if there is a ground fault that the circuit breaker can trip (or fuse blown). The metal chassis of an appliance will be tied to earth for safety reasons.

The earth and neutral are tied together at the panel and nowhere else.

Golfclap

So... Ground and neutral are interchangeable?

Live and neutral carry the normal operating current, earth/ground is for safety.

Neutral is tied to ground/earth at the main breaker panel.

Ground doesn't normally carry any current, but when there's a fault it provides a safe return path for the current. If you have a metal enclosure, it should be grounded, so that if a live wire touches it, it trips the breaker or blows a fuse instead of sitting there hot waiting for someone to touch it.

You can't use neutral for this, because a single point of failure on the neutral line can make the rest of it hot due to electricity conducted through the load.

Some appliances, especially those with plastic cases, don't need the ground wire, because they're double insulated(a single failure won't cause a shock hazard).

Nope...never! The issue is that if you start swapping the ground and neutral you make the ground wire a current conductor and can have parts of an electrical system energized that should not be.

We may only tie the ground and neutral together in the panel and nowhere else in the whole electrical system.

The ground conductor is normally never a current conductor (except for slight leakage). Ground and neutral are both grounded conductors that perform different jobs in an electrical system.

I've been on commercial/industrial service trucks where I've seen a lot of shady stuff with grounding, though.

Power comes in the active and goes out the neutral.

The active has protection on it that causes it to stop the electricity if something goes wrong.

If the active burns off inside an appliance it doesn't have the neutral to take electricity away anymore, it becomes dangerous and can cause the appliance to give you a shock.

The ground wire is connected to the casing of the appliance so that if the above happens, the electricity now has something to take it away and trigger the protection to stop the electricity.