I'm a high school student, just learned relativity.
I understand that observed time is different between two different inertial reference frames. I vaguely understand that time is different in two different non-inertial reference frames. Now consider the following:
A watchmaker makes a watch at reference frame A, with the time of the clock corresponding to the time at reference frame A. They then give the watch to another person at reference frame B. (moving relative to frame A at velocity v)
Does the watch track time correctly for the person at B?
Also, if the systems are non-inertial frames, would the results change?