The only difference is that with Bitcoin nobody has the ability to offer unlimited bailouts to cover unbacked credit.
Yes, this is the crucial difference: FRB + elastic money is a deadly combination.
FRB with gold backed money was common practice so there is no way bitcoin can be immune to excessive FRB.
However, with gold, bankers were using the difficulty of moving around gold inventory as a lame excuse for opacity and fraud.
Conversely, a bitcoin bank could not pretend it cannot deliver bitcoins: that's one of the two reasons a bitcoin banking system will be safer and less prone to excess than the current "debt based" banking system.
The other reason is that a bitcoin banking system rides on top of a p2p system: one can always fall back to being one's own bank.