There are different definitions of money and saving accounts are included in M2 (“money and close substitutes”) but not in M1.
What about time deposits? For short maturities they are included in M3. And what about longer term depositss? Are banks creating money when they lend those out?
You're hanging on to the "banks lend out deposits" mental model. Stop that. The Bank of England has an accessible write-up on this: https://www.bankofengland.co.uk/-/media/boe/files/quarterly-....
Loans create deposits. Whether those deposits then end up in a checking account through a payroll service or a vendor's savings account through a payment for goods and then transfer is irrelevant.
A bank making a loan is trading one asset, cash, for another asset, a loan. If that's "creating money", then doesn't that imply that a loan is "money" and cash is not "money"?
Banks don't lend out balances. "Banks lend out balances" is just an analogy. (It was truer under the gold standard.)
Banks create money through lending and destroy money via write-offs. Periodically (in the U.S., at the end of the day) banks count up what they owe and what they're owed and make sure the ratio is legal. If not, they borrow (from each other or from the Fed) to make up the difference.
(For monetary purposes, savings accounts are checking accounts. Banks don't segregate savings from their balance sheets. Balances in savings account can be withdrawn just as easily as those in checking accounts.)