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David C,

You asked:

Clocksync calls the time it displays  Atomic time. [...] Is Clocksync wrong?

Technically, yes. But, they're not alone. Many people refer to any clock or watch that is upated to match a standard time as "atomic". A Google shopping or Amazon search for an "atomic clock" will return a bunch of radio updated clocks. Of course, what your app, and all of these clocks are displaying is not TAI, but instead the standard time for whatever time zone they were set for. Whether the clock is using NTP or the radio signal broadcast by a timekeeping service, such as NIST, the time they are displaying is an offset of UTC...which, contrary to what the timeanddate website says is 37 seconds behind TAI as of January 1st, 2017. UTC itself is actually an offset of TAI, with "leap seconds" added every so often to keep it within 0.9 seconds of UT1. The last leap second was added at the end of 2016. So, ultimately, the time that all of these clocks are displaying is based on TAI, but is actually an offset of it...usually by some integral number of hours and now 37 seconds. (Some time zones are actually offset an addtitional 30 or 45 minutes.)

UT1 is a time scale based on the actual rotation of the Earth. Observatories all over the globe are constantly determining the orientation of the Earth in space (and thus, solar time) by observing such things as distant quasars. The results of these observations are known as UT0. UT0 is corrected for the motion of the wandering rotational pole of the Earth and the result of that correction is UT1. UTC is an approximation of UT1, but is kept at a steady interval (SI seconds), unlike the variable UT1. The purpose of all of this is to keep our clocks (based on UTC) in close agreement with solar time (UT1). Otherwise, far into the future, the sun would rise at 1200 hrs.

Regards,

Sean C.