Money itself is whatever people choose to use as the general medium of exchange. Money substitutes function as a medium of exchange in lieu of money itself because they are redemption claims to money that can be exercised on demand at par. People will choose whether to use money or money substitutes according to their judgment of the relative advantages and disadvantages as a medium of exchange in the circumstances of their trades.
A particular item can serve as a money substitute as long as it is a redemption claim to money that can be exercised on demand at par. If a bank, then, so redeemed customer deposits that are credit deposits, such as passbook saving accounts, then those deposits are money substitutes. In fact, checking accounts in our day and age are also legally credit deposits. The bank owns the funds in customers’ checking accounts (customers have lent the funds to the bank) and the bank owes the customers immediate payment.
Before the financial crisis starting in 2007 and the ensuing economics downturn, the split between money itself (i.e., Federal Reserve Notes) and checkable deposits was approximately 25% to 75%. During the economic downturn the split moved to 50% to 50% as people desired to hold more cash itself.
The general trend (accentuated by governments), however, has been toward minimizing the use of cash.
This trend toward using money substitutes instead of money does not depend on what money itself is. This trend was also strong under the gold standard. Near the end of the classical gold standard, most transactions were done in bank notes or bank deposits and not in gold and silver coins. Even under a genuine gold standard, people may choose (for convenience, safety, and so on) to conduct the bulk of their transactions in money substitutes.
No matter how far this trend goes, it does not result in the money substitute becoming money. Its use as a medium of exchange remains entirely depend on redemption on-demand and at-par for money itself and thus, on the continuing existence of money. In order for the item used as a money substitute to become money, the government must either initiate legal disabilities against money itself or legal privileges for money substitutes.
Take a look at Rothbard on the history of switching monetary regimes.