That's how the banks explain it, but it's somewhat misleading.

The loans come before the deposits. When someone takes out a loan, the bank creates 2 ledger entries. On the asset side is the loan, where you owe the bank the amount of the loan plus interest. On the liability side is the bank deposit that's created in your account, where the bank owes you the amount of the loan. That's all a bank deposit is, a bank IOU. You're an unsecured creditor of the bank.

The bank doesn't loan out deposits. They create deposits by making the loan. That's all new "money" (debt) that didn't exist before, the bank just created it out of thin air and charges you interest for the privilege of using it.

If you bring money from another bank to deposit, as for example a check, the bank doesn't hold that deposit in an account with the other bank. The banks settle up with each other using base money, so physical cash or bank reserves. Bank reserves are a special form of money equivalent to cash, held at banks' accounts at the Fed, and that's how banks pay each other. They don't accept another bank's IOUs as payment the way the serfs do.

So when you bring cash or a check from another bank to deposit, all that happens is the bank adds that cash or bank reserves to their pool of reserves, and creates a bank deposit (bank IOU) in your account instead. It has no bearing on the bank's ability to make more loans the way the classic fractional reserve banking explanation suggests.

It theoretically could increase the bank's capacity to make loans if banks were legally required to hold a certain percentage of reserves against their outstanding loans. But the US bank reserve requirements were lowered to 0 in 2020 and are still at 0 today. So banks can continue to create an infinite amount of new "money" by making loans, legally.