Mass or Energy may be stored in various forms but they ultimately have the very same impact on the space-time curvature and other things some of the form of mass and energy look more like mass, others look like what we used to call Energy but there's only one type of quantity that curves the space-time and one quantity that is conserved.
Gravitational time dilation occurs because objects with a lot of mass create a strong gravitational field. The gravitational field is really a curving of space and time. The stronger the gravity, the more spacetime curves, and the slower time itself proceeds.
