A Retail & Commercial bank is a for-profit financial institution that is licensed to accept checking and savings deposits and make loans.
A Credit Union is a non-profit money cooperative whose members can borrow from pooled deposits at low interest rates. In other words a credit union is created, owned, and operated by it's members (depositors), similar to a co-op.
A Savings & Loan Association is owned by their customers or community, and can provide checking accounts, personal loans, and home mortgages.
You may see some financial institutions are insured by the FDIC for up to $250,000 per depositor. The Federal Deposit Insurance Corporation (FDIC) is part of the federal government and is the primary federal regulator of banks. The FDIC insures the savings of millions of Americans and creates regulations and safeguards to prevent bank failures. Meaning if your bank were to close, the FDIC would ensure you didn't lose any money.