Banks still need their books to balance. That means that their liabilities can not exceed their assets. A bank can be solvent on paper but if there was a rush to withdraw by their customers, they may not be able to pay cash for all withdrawals because that cash would be tied up in loans.
In the Tether case it isn't that they loaned out the money they took in, rather their liabilities exceed their assets. Thus Tether is bankrupt on paper. And if everyone tried to withdraw their assets, they would also not be able to pay everyone back.
Thus banks may be illiquid with a balance sheet that ultimately balances (e.g. not bankrupt), but tether is both bankrupt and likely also illiquid because of the 850M loan fiasco.
I swear tether is like Wiley Coyote who has run off a cliff but hasn't yet looked down. I question my sanity a little bit because I do not understand why tether isn't completely disreputable at this point, I must be missing something.