The yield takes compounding into effect, the rate does not. For small rates, e.g. what you get in a savings account, these will be virtually identical. You can start seeing the difference on larger interest rates.
Example: a savings account with $10,000 and a 10% APR (rate). Let us assume you deposit it at the beginning of the year and never withdraw. If the bank only calculated interest once, at the end of the year, you’d get $1,000 interest and the yield would also be 10%.
However, banks usually compound more frequently – in this example, I’ll calculate monthly compounding. After the first month, you get $83.33 interest. Now your balance is 10,083.33. The next month, you get a little bit extra! $84.03 to be precise. Now you have $10,167.36 in your account, and the following month your interest is $84.73. It keeps going up. At the end of the year, you will have a total of $11,047.13 in your account, which as you can see is a little bit more than the $11K you’d have with compounding once. That means the YIELD is actually higher than the rate. To calculate the yield, divide your final interest by the original total, which gives you a APY of ~10.47%, slightly higher than the 10% APR.
Compounding daily would increase the yield ever so slightly, to ~10.52%.
This number is often used as a marketing advantage. When you’re lending money, e.g. depositing into a savings account, it’s more enticing to you if the bank advertises APY (a higher percentage). When you’re borrowing money, e.g. a mortgate or auto loan, it’s more enticing to you if the bank advertises APR (a lower percentage).