The main difference between yields and interest rates is that each term refers to different financial instruments. Yield commonly refers to the dividend, interest or return the investor receives from a security like a stock or bond, and is usually reported as an annual figure. Interest rate generally refers to the interest charged by a lender such as a bank on a loan, and is typically expressed as an annual percentage rate (APR).
For example, if PepsiCo pays a quarterly dividend of 50 cents and the stock price is $50, then the annual dividend yield would be 4% [(50 cents x 4 quarters) / ($50)]. Therefore the current yield is 4%. If the stock price increases to $100 and the dividend remains the same, then the yield becomes 2%. (Bond yield is a bit more complex  if you want to learn about it take a look at our tutorial: Bond Basics: Yield, Price And Other Confusion.)
As an example of interest rates, suppose you go into your bank to borrow $1000 for a new bicycle and the bank quotes you a 5% interest rate on your loan. If you borrow this amount for one year, the interest you would pay on top of paying back the $1000 would be $50 (simple interest: $1000 x 0.05). If the interest rate is compounded then the interest rate you will pay would be a little bit more. Lenders charge interest to compensate for the opportunity cost of not being able to invest it somewhere else. (To learn on compound interest, see Accelerating Returns With Continuous Compounding.)
This question was answered Joseph Nguyen.

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Yield
The income return on an investment. This refers to the interest ... 
Current Yield
Annual income (interest or dividends) divided by the current ... 
Bond Yield
The amount of return an investor will realize on a bond. Several ... 
Indicated Yield
The dividend yield that a share of stock would return based on ... 
Yield On Cost  YOC
The annual dividend rate of a security divided by the average ... 
Interest Rate
The amount charged, expressed as a percentage of principal, by ...