Mortgages are an easy way to explain this, because they have other fees besides interest. A mortgage could include closing costs, private mortgage insurance, and application fees, to name a few potential extras. A mortgage's APR includes those extras. That means even though a mortgage may have an interest rate of 6.7%, the mortgage APR could be 6.8%. Use our mortgage calculator to calculate your monthly payment.
However, with credit cards, APR and interest rate are interchangeable. Even if your card charges an annual fee, that's not a cost associated with borrowing money. The only borrowing-related charge your credit card uses is interest, which makes the APR and the interest rate the same thing.