Q:

How can two identical clocks show different time (in case of time dilation)

Pardon my ignorance, if we have two identical clocks and we use them to measure time dilation. 
Suppose we have two identical clocks one in a Satellite around the earth and one on the ground. Now the clocks are mechanical and consist of moving parts. Does the clock in the satellite run faster because it's parts are turning slowly? Or does this have to do with the observer on the ground seeing the clock turning faster due to the amount of time it takes from the clock to reach the observer on ground. 

A:

Time dilation is not a result of the time light rays take to reach us from the dilated objects.
Physicists have a tendency to be lax about terminology and talk about seeing a clock run slowly when they should say observing a clock run slowly. The word observing means determining the behaviour after effects like the travel time of light to our eyes have been accounted for. We observe the clock on a satellite to run faster than one on the Earth's surface meaning it really does run faster.
Gravitational time dilation is a fundamental effect due to the geometry of spacetime. Clocks really do run more slowly on the Earth than at the altitude of a satellite. This affects everything, so for example a radioactive material will decay more rapidly at a higher altitude.

