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Interest rate is more generic.

If your interest rate is 1% per month, your APR will be more than 12% per year because of compounding.

If you pay points on a mortgage to get a lower interest rate, your APR will be higher because the points cost and other fees will be amortized over the life of the loan.

APR tries to give you a standard way to compare the costs of borrowing for different types of loans with all sorts of gimmicks.

http://en.wikipedia.org/wiki/Annual_percentage_rate

Note that there will be a legal definition for the

effective APRin your jurisdiction.