There are various types of second home mortgages. The main differences are in the way you receive the money. With a standard home equity loan, you receive a one-time lump sum. Then, you repay it over time. Usually, you pay monthly fixed payments. Variable-rate loans are also available, but variable rates are more common with home equity lines of credit. A home equity line of credit (HELOC) is a pool of money that you can draw from. You are not actually required to withdraw from that pool at all, but you can whenever you decide you need it. The lender will set a maximum limit and you can borrow as many times as you'd like until you reach that limit. HELOCs are similar to credit cards in that you can keep repaying and borrowing continuously.
Most HELOCs are second home mortgages. However, some are first mortgages. For instance, you can get a HELOC on a home that you own outright. In that case, it would be a first mortgage.