For all intents and purposes to the consumer, there is little difference among thrifts, commercial banks, and credit unions. The financial services they all offer will be similar and you probably don’t even know if the financial institution you’re banking with is a thrift or commercial bank (Washington Mutual  is technically a savings and loan and the largest one). In fact, the only real notable difference between thrifts/banks & credit unions has to deal with depository insurance. Thrifts and commercial banks are covered by FDIC, credit unions are covered by NCUA, though both are covered to the same limit of $100,000 per person per financial institution.
Now, for the academics and trivia buffs out there, here’s a little more on their differences.
Thrifts, probably better known as savings and loan institutions (mostly because of the S&L crisis  in the 1980s and 90s when 747 banks failed), originated as institutions that deal only with savings accounts and mortgage loans (hence savings & loans). Nowadays, they’ve broadened their financial offerings such that the only differences are in business dealings. By law, thrifts may lend up to 20% of their assets to commercial loans and only half of that can be used on small business loans. Also, in order to obtain advances from the Federal Home Loan Bank, thrifts must meet a ‘qualified thrift lender test.’ That test requires that 65% of its assets must be in mortgage and consumer-related assets. In plain English, they’re just restricted to keeping most of their lending in the mortgage and consumer arenas.
By the way, IndyMac Bank was a thrift bank and the largest at the time it failed (it was also the second largest bank failure ever, second to Continental Illinois Bank in 1984)
A credit union is cooperative bank that is privately owned and controlled by its members, the account holders. The purpose of the cooperative is to provide credit and financial services at reasonable rates and that’s why you’ll often find better loan rates at credit unions. Another requirement of credit unions is that there must be a restriction on who can join based on its “field of membership.”
What’s also interesting about credit unions is that each depositor is given a vote in the board of director elections and each member is considered an “owner” of the credit union. The elected board of directors is charged with the responsibility of setting policies governing interest rates and other services.
Other than that, the only other major difference is in vocabulary. A savings account is called a share account, a checking account is called a share draft account, and certificates of deposit are known as share term certificates. The “share” is a reminder that everyone is an owner in the union.
Lastly, deposits are insured by the National Credit Union Administration up to $100,000.
A commercial bank is “everything else.” The term is really just a way to distinguish a bank as most consumers recognize it (savings and checking accounts, ATMs, etc.) from an investment bank, like a Merill Lynch or a Lehman. As I mentioned before, the deposit insurance that governs your assets at these banks is the FDIC and that covers you up to $100,000 (there are certain ways to extend that limit).
Those are the basic differences from a layman’s perspective, there are actually far more differences when you get into the specifics (here’s an intriguing Economic Letter out of the Federal Reserve Bank of San Francisco detailing some differences between bank charters and thrift charters ). I skipped over those because they weren’t as interesting and didn’t really have much bearing on how consumers are affected.