Time is what we humans use to measure the passing of events. There is probably no change without the concept of time, and time probably implies memory.
Time is a unit of measure but the process of measuring time must not be confused with time itself, because it takes "time" to measure time. We would not want to measure distance with a rubber ruler and we should not measure time with a rubber clock. (Einstein did just that !)
Absolute clock time must be referenced to a fixed point. i.e. clock time on the moon has no meaning. What about UTC on the moon? UTC implies a reference position.
Elapsed time on the moon does have meaning and with a proper supply of cesium atoms, it could be measured and assuming that external fields such as gravitation and radiation have no effect on cesium, would coincide with similiar events on earth.
The UTC second has been defined by the 13th General Conference of Weights and Measures in 1967 as "The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom." This, of course, means that one billionth of a second is unmeasurable (to that same precision) because a little more than one ten-millionth of a second is the defining granularity of our measuring device.
How can you measure variations in the clock frequency?
Given two clocks that vary, how do you determine which one is correct?