I think I follow this and most people probably also understand what it is that causes a bank default (i.e. everyone withdraws their money simultaneously). Still trying to dig at the mapping.
IIUC the main difference with stock is the market prices the items by demand unlike where the treasury effectively prices the items by supply and banks work under that. So the stocks are expected to always be liquid potentially at a lower price while banks have to be bailed out by the government for liquidity if a bank run. This definitely feels different, though I guess the extreme case gets closer, if every single bank needs to be bailed out at once, the currency price will go down like stocks do.