That is right each cell of a DRAM uses a transistor and a capacitor. Common circuits for a number of cells are required to charge, discharge and read the capacitor charge. Also the charge stored in the capacitor will need to be refreshed very often. So as not to loose the data when the necessarily small capacitor gets discharged.
Static memories uses more transistors but do not depend on a charge stored in a capacitor to hold the data. So they dont need refreshing.