A remortgage is when you replace your existing mortgage with one lender to one with another lender on the same property, perhaps to get a better deal or to borrow more money. If you transfer your existing mortgage terms to your onward purchase that is called porting. A home mover mortgage is a term to describe a new mortgage taken out by a home mover on their onward purchase.
When borrowing more money please note you should think carefully before securing other debts against your home. Your home may be repossessed if you do not keep up repayments on your mortgage.