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.

The UK ended up owning RBS: https://commonslibrary.parliament.uk/royal-bank-of-scotland-...

Ireland got hit pretty hard: https://www.irishtimes.com/business/financial-services/2022/... but did at least manage to send Sean Quinn to actual jail.

Cyprus had too large and too dodgy a banking sector for its government to cover, so there depositors did incur real losses ("haircut").

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%

>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.