The interest rate is the cost of borrowing expressed as a percentage of the loan. The monthly payment is the actual dollar amount you pay each month, which is determined by the loan amount, the rate, the term, property taxes, insurance, and mortgage insurance if it applies.
Two loans can carry the same rate and produce very different payments. A longer term spreads the balance over more months and lowers the payment. A smaller down payment can trigger mortgage insurance that adds to it. Taxes and insurance vary by property and can swing the payment more than a small rate difference.