The difference between APR and interest rate on a personal loan is that the APR includes fees while the interest rate does not. Both the interest rate and the APR measure the cost of borrowing over a year's time, and both are expressed as a percentage rate. While these terms are fundamentally different, they are often used interchangeably and can be equal in cases where the loan has no fees.
One situation where the APR on a personal loan would be higher than the interest rate is if the lender has an origination fee whose cost is spread out over the life of the loan. An origination fee is a charge for initially processing the loan. Many lenders make you pay the fee upfront or deduct it from the amount you receive, in which case the cost is not included in the APR. However, other lenders divide up the cost of the origination fee between your payments. In that situation, your APR is your interest rate plus the yearly cost of the origination fee.
Here's an example from the lender FreedomPlus: A borrower's interest rate could be 15.49%, but their APR might be 18.34% because of the origination fee. Certain lenders may charge other fees that get included in the APR as well, but it's unusual to see anything other than an origination fee with personal loans.