Payment and payoff date are separate choices
Mortgage payments are amortized: interest is charged on the outstanding balance, while principal reduces it. Restarting a 30-year loan after several years can lower a payment partly by spreading debt over more months.
Illustration: a homeowner with 26 years remaining can compare a new 30-year term with a 26-year same-payoff-date term. The first may improve monthly cash flow; the second is a cleaner comparison of rate savings.