Whether you realize it or not, by holding money you are saving; and in doing so you are funding the institution that supplies the monetary instruments you hold. That you do so to supply yourself with exchange media doesn't matter. 1/

Banks exist precisely for the sake of converting the public's demand for exchange media into a demand for their IOUs, so they can take advantage of that demand to fund their investments. To do this they must make their spendable IOUs more attractive than "base" exchange media. 2/

Although it is true that any individual may not hold his or her bank-money balances for long, they are saved, and represent a loan to the issuer, for as long as they are held. Banks rely on the law of large numbers to have a reliable pool of such savings available at any time. 3/

The holding of, say, gold coin balances in a gold standard regime is also saving. The difference is that it represents saving, but not lending. 4/

So any "confusion" is on the part of those who imagine that people must _either_ save or hold money balances.