I am not sure there is a clear distinction between the two for fractional reserve banking ?
The bank can have done nothing "wrong", yet if the situation is bad enough : bank run + entities it has been lending to going bankrupt + entities that could bail it out going bankrupt too ; then the bank IS going bankrupt, and taking most of the opposite fraction of the money it claimed to "hold" with it...
This is where the "lender of last resort", i.e. the government, comes in. Depositor losses are sufficiently bad for the economy as a whole that it makes sense to prevent them at almost any cost.
>I am not sure there is a clear distinction between the two for fractional reserve banking ?
If your assets are real and not shitcoins, there is a difference. If I have $200 in my bank, the bank takes $100 from me and buys AAPL stock (and adds their own cash); and then I go to withdraw my $200 on Saturday:
1. The bank is illiquid. I want $200 cash, but the bank only has $100 and 1 AAPL stock.
2. The bank is (likely) solvent. Unless AAPL crashes below $100 on Monday morning they are likely good for the money (AAPL, a blue chip stock, is unlikely to crash below $100) on monday morning. In this case a lender of last resort will step in (like the Fed) and bank may pay some premium for an emergency loan.
It's statistical, like everything, and the difference is whether you have a guaranteed valuation for your illiquid assets. If you are backed by the full faith and credit if the US (taxation, IRS, and military), you are 99% solvent. In Brazil, maybe 80%
The bank can have done nothing "wrong", yet if the situation is bad enough : bank run + entities it has been lending to going bankrupt + entities that could bail it out going bankrupt too ; then the bank IS going bankrupt, and taking most of the opposite fraction of the money it claimed to "hold" with it...