According to Investopedia the two most common types of mortgages in the United States are fixed rate and variable rate (also called adjustable rate). With a Fixed Rate Mortgage, the interest rate does not change for the entire loan term. The distinguishing factor of a fixed-rate mortgage is that the interest rate over the time period of the mortgage is the same as when the mortgage is originated.
With a Variable Rate Mortgage the interest rate is not fixed. The interest rate adjusts periodically. Monthly principal and interest payments change according to a predetermined schedule throughout the life of the loan.