Gravitational time dilation and time dilation, as described in the context of special relativity, are both manifestations of the same underlying phenomenon: the relative passage of time depending on the gravitational field or relative motion between observers. While they have some similarities, there are fundamental differences between gravitational time dilation and time dilation due to relative motion.
Gravitational time dilation refers to the effect of gravity on the passage of time. According to general relativity, the presence of a massive object, such as a planet or a star, curves the fabric of spacetime. This curvature causes clocks in stronger gravitational fields to run slower relative to clocks in weaker gravitational fields. In other words, time appears to dilate or stretch out in the presence of a stronger gravitational field. This effect has been confirmed by experiments such as the Pound-Rebka experiment and the observations of gravitational redshift.
On the other hand, time dilation due to relative motion, often referred to as "special relativistic time dilation," is a consequence of the theory of special relativity. It states that the relative motion between two observers will result in a difference in the perceived passage of time. When two observers are moving relative to each other at speeds close to the speed of light, they will experience time dilation. This means that time appears to pass slower for the moving observer compared to the stationary observer.
While both gravitational time dilation and time dilation due to relative motion involve a change in the perception of time, they arise from different physical phenomena: gravity and relative motion, respectively. Gravitational time dilation is associated with the curvature of spacetime caused by massive objects, while time dilation due to relative motion is a consequence of the constancy of the speed of light and the principles of special relativity.