This paper explores an essential but neglected aspect of recent discussions of the banking and financial system, namely money itself. Specifically, I take up a distinction drawn by Susan Strange which has never been fully elaborated: between a financial system that is global, and an international monetary system that remains largely territorial. I propose a sociological elaboration of this distinction by examining each category, ‘finance’ and ‘money’, in terms of its distinctive orientation to risk and debt. Money is distinguished by its high degree of liquidity and low degree of risk, corresponding to expectations that derive from its status as a ‘claim upon society’– a form of socialized debt. But as Strange argued, these features of money are being undermined by the proliferation of sophisticated instruments of financial risk management –‘strange money’– that, as monetary substitutes, both weaken states' capacity to manage money, and more broadly, contribute to ‘overbanking’. The ultimate danger, according to Strange, is the ‘death of money’. The paper concludes by exploring the implications of the distinction for sociological arguments about the changing nature of money.