A question about earth ground and current loop
What is different is that for a battery there is not other connection to ground, this is not the case with the mains.

In the mains, the neutral connection is actually grounded as it enters your building, or at the transformer. 

As such shorting the live wire to the case is really shorting the live wire to the neutral side of the transformer through the ground line creating a loop, and, as you have expressed, large current flows till the fuse of breaker trips.







simulate this circuit &ndash; Schematic created using CircuitLab

Which is why this is dangerous...



With an isolation transformer you isolate the power from ground and there is no return path.