In today’s fractional-reserve banking systems, the government (through its central bank) prints money. Dollar bills are printed by the Federal Reserve System, Euro bills are printed by the European Central Bank, Yen bills by the Bank of Japan, and so on. Printed money is sometimes called currency or cash.
Commercial banks do not print or create money. Commercial banks create checking account balances for customers. The reason checking account balances are accepted everywhere as a medium of exchange is that banks always stand ready to redeem the account balances of their customers for cash money on demand at par value. So checking account balances are money substitutes, but not money itself.
Commercial banks are required by the government’s central bank to keep a fraction of the total checking account balances they issue to their customer as reserve, which can be cash, on hand. If the reserve ratio is 10%, then a commercial bank can have 10 times the amount of checking account balances as reserves.
If a commercial bank acquires $1,000 in cash as reserve, then it can issue $10,000 in new checking account balances to its customers. The simplest way for a bank to do so is to extend new loans to its customers and put the loan amounts in their checking accounts. So, banks create new money substitutes (by creating credit or loans) but not new money.
Take a look at Murray Rothbard’s treatment of the money inflation process in his book, The Mystery of Banking.