Apart from rushing trains and moving platforms, of course at relativistic speeds which we encounter every day, I wonder whether there is any practical use/ application where asynchronous clocks play some role.

In reply to Klaus’ comment, I would guess that a current application of these concepts, is that cosmic phenomena need to be translated from Hubble Telescope perspective to a sidereal perspective (relative to distant stars) in efforts to map out how something would look with no relative motion.

This explanation somehow was much more intuitive for me when I considered that someone sends a signal from the center of the train to both ends of the train at light speed. Because the train is moving at some speed relative to the platform, the signal will arrive at the back of the train first (because that side is moving towards the light signal) and the signal will arrive at the front of the train second (because that side is moving away from the light signal).

From the perspective of Team Train Team Platform is rushing by so Team Platform has longer seconds so longer metres so Team Platform measures a shorter train. If Team Train considers that Team Platform is rushing by, then Team Platform knows that Team Train will have shorter seconds so Team Trains metres are physically shorter thus the value that Team Train will get between the 2 marks will be more metres and so they (Team Train) will report a longer train.

In fact the distance between the marks from the platform perspective will be even longer than the “rest length” of the train because when the sprays are fired the railway passing by under the train is length contracted so the distance will be “amplified” when measured from the railway (platform) frame of reference

Two clocks are asynchronous if they do not depend on each other, for example two free-standing oscillators at the exact same frequency will still be asynchronous, since you will always have a small amount of drift and an unknown phase at startup.