British money is - or was - explicitly an IOU. The notes bore the phrase "I promise to pay the bearer on demand the sum of (n) pounds ..." Used to be gold, not sure what you get these days. Other countries also, like India.
Even the term "banknote" makes it explicit: a note (of credit) issued by the central bank.
Coins are not formally IOU's, because historically they had intrinsic value.