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).