Time dilation due to gravity, known as gravitational time dilation, differs from time dilation caused by motion, known as velocity time dilation, in its underlying cause and manifestation.
Gravitational time dilation occurs as a consequence of the curvature of spacetime caused by massive objects. According to Einstein's theory of general relativity, massive objects like planets, stars, or black holes distort the fabric of spacetime around them. The stronger the gravitational field, the more spacetime is curved. As a result, the flow of time is affected, and clocks closer to the source of gravity appear to tick more slowly relative to clocks farther away.
Velocity time dilation, on the other hand, arises from the effects of special relativity, which describes the behavior of objects moving at high velocities relative to each other. According to special relativity, when objects move relative to each other at speeds approaching the speed of light, time appears to pass more slowly for the moving object compared to a stationary observer.
The manifestation of these two types of time dilation is slightly different. In the case of gravitational time dilation, an observer in a stronger gravitational field (e.g., near a massive object) will experience time passing more slowly relative to an observer in a weaker gravitational field (e.g., farther from the massive object). This effect is observable even for stationary observers and is independent of their own motion.
Velocity time dilation, on the other hand, is dependent on the relative motion between two observers. An observer in motion relative to a stationary observer will perceive time passing more slowly compared to the stationary observer. However, from the perspective of the moving observer, it is the stationary observer who appears to be experiencing time dilation.
Both gravitational time dilation and velocity time dilation have been experimentally confirmed. For example, the gravitational time dilation has been observed in experiments involving precise atomic clocks placed at different altitudes, where the clock at the lower altitude (closer to Earth's gravitational field) runs slightly slower. Velocity time dilation has been measured in particle accelerators, where high-speed particles with short lifetimes are observed to decay more slowly from the perspective of a stationary observer.