No Cost refinance - closing costs are rolled into the loan, no cash needed from borrower. Really not a no cost, more accurately a no cash.

No Cost refinance - using Lender Credit to pay closing costs. If current market rate is 3.5%, you accept a higher rate, say 3.625%, and the bank provides a lender credit to pay closing costs. Not really a no cost, the cost is accepting a higher than market rate. However, a great tool to use, as there is no cash from borrower and no costs rolled into the loan.

If the Consumer Finance Protection Bureau wants to do its job correctly, they'll ban phrases like "no cost refinance" as being, at the very least, confusing. It's actually "no UPFRONT cost refinance." Of course there's a cost in there somewhere, as described by crackdclaw.