The normal definition of money includes bank balances.
If you deposit $1000 of cash at a bank, and they loan it to someone else, you still have $1000 of money but now that other person also has $1000 of money.
But the abstract (and more accurate) version is even more interesting. Let's assume the person getting the loan deposits the money at the bank. Now we don't even need to touch cash. Giving out a loan is just adding 1000 to someone's account balance, in exchange for their contract to repay $1000+interest later.
A bank can do this over and over, and each time it creates $1000 of money. And when the loan is repaid, the money disappears.
Loans create deposits. (When you're approved for a loan, the bank makes the numbers in your account go up.) Banks don't lend out deposits.
See: https://www.bankofengland.co.uk/-/media/boe/files/quarterly-...