What is the difference? I understand the neutral goes on the neutral bar and the same for the ground wires but if you were to check continuity between the neutral bar and ground bar they are connected. Can you explain?

The neutral and equipment ground, and the grounding electrode conductor all join at only one location, the box that contains the main switch. There are point allowed to be grounded ahead of the main switch, but typically performed at the main.

From this point on, to outlets and to "sub" panels, the neutral and ground are separated. The neutral is current carrying, even thou it is grounded. The equipment ground is the safety return from the metal cases of appliances, stands to reason if a unit will fail and short out it would energize the metal case posing a shock hazard without the equipment ground.etc.

The equipment ground needs to be a good solid conductor back the main neutral/ground connection. It needs to be low impedance (AC resistance) to allow the current to rise very high very quickly so the circuit breaker or fuse sees an abnormal amount of current, and react appropriately, open due to heat created by the high current. A good grounding system will insure that overcurrent protection devices will operate quickly measured in cycles or milliseconds.

So the equipment wire sits there doing nothing until something shorts out, the neutral is part of the normal circuit and always carries current as the return for a circuit, when there is a load. This current is not wanted or allowed on the equipment ground, except in only 3 or 4 special reasons.

Hope this makes sense.