Mortgage refinancing is used to lower the interest rate of a home loan. It involves replacing your current debt with a new one, which may result in a lower monthly payment, canceled insurance premiums, and different repayment terms.
Home equity is the amount you have paid off on your home by now. When you have positive home equity, the amount you owe on your mortgage is less than the fair market value of your house. A home equity loan is when you use the equity you own in your house as collateral.
A reverse mortgage is only for those who are at least 62 years old and is very similar to a home equity loan. It can be used to supplement one's retirement income, offering either a line of credit or a fixed monthly payment to be paid back when the borrower moves away, sells the home, or passes away.