Observed time dilation and actual time dilation are two ways of looking at the same phenomenon, but they arise from different perspectives and reference frames.
In the theory of relativity, time dilation refers to the difference in the passage of time between two observers who are in relative motion or in different gravitational fields. The term "observed time dilation" is used to describe the measurement or perception of this time difference by one observer relative to another.
When two observers are in relative motion or located in different gravitational fields, they will measure the passage of time differently. From each observer's perspective, the other observer's clock will appear to be running slower compared to their own. This is observed time dilation, as each observer perceives the other's time as dilated or stretched out.
On the other hand, "actual time dilation" refers to the physical phenomenon itself, independent of any particular observer's perspective. It refers to the objective difference in the rate of time passage between two reference frames that are in relative motion or experiencing different gravitational potentials.
In essence, observed time dilation reflects the subjective experience of time difference between observers, while actual time dilation represents the objective reality of time passing at different rates. Both perspectives are valid and consistent within the framework of relativity, but they offer different viewpoints on the same underlying phenomenon.