Every larger payment brings the same question from the bank, and both answers sound sensible. The difference in interest can be several times over, but it is invisible until you work it out. Below is the same loan settled both ways.
Shortening the term saves 169 298,86 zł in interest and ends the loan 101 instalments sooner. Lowering the instalment saves 57 935,57 zł and takes 359,80 zł off the monthly payment.
Interest accrues on the principal and over time. An overpayment always removes principal, so it saves in both cases -- but shortening the term also removes time, while lowering the instalment keeps the same schedule and simply spreads a smaller debt over the same years. That is why the first is cheaper and the second frees up more each month. These are two calculations side by side, not advice.
Equal instalments, a fixed rate for the whole term, the overpayment made in one go now, no early-repayment fee and no insurance added to the instalment. On a variable rate this answers what would happen if the rate held, not what will happen.
Shortening the term keeps more interest in your pocket, because it also removes the time over which interest accrues. Lowering the instalment saves less but frees up more every month. The calculator shows both figures; which one suits you depends on whether the monthly payment or the total cost is the problem.
By default most banks lower the instalment, because that needs no amendment to the contract. Shortening the term usually has to be stated explicitly when you make the overpayment, sometimes in writing. Worth settling before the transfer.
On a Polish variable-rate mortgage an early-repayment fee is only possible during the first three years and is capped by law. The calculator does not include one: if your contract has it, subtract it from the saving.
Yes, though less than people expect. Interest accrues on the balance daily, so paying just before the instalment is charged works a few days earlier than paying just after. For a one-off overpayment that is worth about one interest charge, not the difference between the two options.