Einstein's theory of special relativity indeed includes time dilation effects between moving and stationary objects. However, it's important to note that time dilation is not limited to this scenario. Time dilation can occur in various situations where there is a difference in relative motion or gravitational potential.
In the context of special relativity, time dilation occurs when an observer measures time differently between two relatively moving objects. If an observer is moving with respect to a stationary clock, they will perceive that clock as running slower compared to their own clock. This effect is known as time dilation and is a consequence of the fundamental postulates of special relativity.
Regarding your second question, the perceived difference in the passage of time when we sleep compared to when we are awake is not an example of time dilation as described by special relativity. Instead, it relates more to our subjective perception of time and the different states of consciousness. When we are asleep, our awareness and perception of time are diminished, and it can feel like time passes more quickly or more slowly depending on our dreams or the depth of our sleep. However, from a physical standpoint, time itself is not actually dilated or altered.
It's important to differentiate between time dilation as described by special relativity, which is a well-established scientific phenomenon observed in experiments, and the subjective perception of time, which can vary based on individual experiences and states of consciousness.