The interest rate prices the balance. The APR folds lender cost into one annualised figure. Neither number answers the question on its own.
The interest rate is the simpler of the two. It sets what the lender charges on the outstanding balance, and it is the number that drives your monthly principal and interest payment. Nothing else.
The APR takes that rate and adds the cost of getting the loan: origination charges, discount points, mortgage insurance where it applies, and some third party fees. It then spreads that cost across the full term and expresses the result as one annualised percentage. Because the fees are amortised over the whole term, the APR is always at or above the rate on a loan that carries any cost at all.
That makes the APR useful for one specific job: comparing two offers for the same loan amount, the same term and the same product. If one lender quotes a lower rate but a materially higher APR, the difference is sitting in the fee column, and page two of the Loan Estimate will show you where.
It is less useful in three common situations. It assumes you hold the loan to term, so it understates the cost of points if you sell or refinance in year six. It treats a fixed loan and an adjustable loan differently enough that cross comparison is misleading. And it excludes several real costs, including most title and escrow charges you shop for yourself.
A worked illustration, using sample figures only. On a $400,000 thirty year loan, a rate of 6.500% with $6,000 of lender cost produces an APR near 6.63%. The same rate with no lender cost produces an APR equal to the rate. The gap between the two columns is the fee, annualised. Read both numbers, then go and look at the fee itself.
Illustrative sample figures for a template demonstration. Not a rate quote, not an offer to lend, and not live market data.