[lukevp]

When you refinance, it’s just a new mortgage. You can do it purely for rate, or you can do a cash out refi (refinance at market rate for your house, pocket the equity you’ve built up as cash, but now your loan is bigger). The loan terms are like a regular mortgage, because they basically are. The originator of the mortgage often sells it on the secondary market.

[gambiting]

Well yes, obviously - it's the same here. I just read what OP said as a requirement that you have to extend your mortgage by another 30 years. Here you just get a now mortgage of any length you want - if you fancy 9 years or 12 or 38 that's fine.

[frumper]

Extending isn't the right word. You're applying for a completely new one, often with a different bank. The common options are 15 year and 30 year terms. The new one pays off the old one and if it's structured you can even get extra cash out, though that may increase your interest rate.