Time dilation due to special relativity (SR) and time dilation due to general relativity (GR) are indeed two separate phenomena, although they can be related in certain scenarios.
Special relativity deals with time dilation caused by relative motion between observers. According to SR, time dilation occurs when an observer is in motion relative to another observer. The faster the relative velocity between the observers, the greater the time dilation effect. This effect is independent of gravitational fields and depends solely on relative velocities.
General relativity, on the other hand, incorporates gravity and describes the curvature of spacetime caused by mass and energy. In the presence of a gravitational field, time dilation occurs due to the curvature of spacetime. Clocks located at different distances from a massive object will measure time at different rates. The stronger the gravitational field, the greater the time dilation effect.
When considering both SR and GR effects in the same reference frame, the combined time dilation can be calculated by taking into account the effects of both relative motion and gravitational fields. The calculation involves using the appropriate mathematical equations for each scenario and summing the contributions.
In most everyday situations, the effects of time dilation due to relative motion are negligible compared to the effects of time dilation caused by gravity. For example, the time dilation experienced by an object in motion at speeds typically encountered on Earth is extremely small compared to the time dilation caused by the Earth's gravitational field.
However, there are extreme cases where both SR and GR effects need to be considered, such as near black holes or in highly precise experiments involving atomic clocks or satellite systems like GPS. In these scenarios, the effects of both relative motion and gravitational fields are significant, and the combined time dilation must be taken into account.
In summary, SR and GR time dilation are separate phenomena caused by different factors (relative motion and gravitational fields, respectively). While they can both contribute to the overall time dilation in certain situations, they are typically treated as distinct effects that need to be considered separately.