APR and APY are both annual rates, but they answer slightly different questions. APR, annual percentage rate, is the simple yearly rate before compounding, and by law it includes certain fees on loans. APY, annual percentage yield, is the rate after compounding, showing what you actually earn over a year. Savings accounts advertise APY because it is the bigger number; lenders quote APR because it is the smaller one.
The gap grows with the frequency of compounding. A savings account paying a 4.00% rate compounded daily has an APY of about 4.08%. On $20,000, that is $816 of interest over a year rather than $800. Not dramatic, but real.
On the borrowing side, a credit card with a 24% APR compounds daily, so carrying a balance for a year actually costs about 27%. The APR understates the true cost, which is exactly why cards quote it that way.
When comparing two savings accounts, compare APY to APY. When comparing two loans, compare APR to APR, and note whether fees are included. Mixing the two makes a savings account look worse or a loan look better than it is.
The common mistake is seeing a headline rate and not checking which one it is, or ignoring the conditions attached: many high-APY accounts require a minimum balance, direct deposit, or apply the rate only to the first few thousand dollars.