“Free switch” means the new lender will generally cover legal and appraisal costs. That’s opposed to a refinance, where legal fees (and often appraisal fees) apply. The lender losing the mortgage will typically charge the borrower a discharge fee in either case.
Free switches usually apply only to straight transfers (where there’s no increase to mortgage amount or amortization).
If your current mortgage has a line of credit attached, you must refinance when changing lenders. Free switches do not apply.