What cause the difference in communication delay, about 11 seconds in this video:
and apparently almost no delay on this one:
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I think there's a bit of an X/Y problem here -- the question you're asking isn't really the question you want an answer to.
First, a direct answer to the question you're asking:
The long delay is chiefly a result of several sources.
Starting from the ISS, you have a delay from the video encoder on board, you have a delay from the satellite downlink that goes from ISS to a TDRS satellite, down to the TDRS terminal at White Sands, New Mexico, you have a delay from the TDRS terminal to the video processing facility at JSC building 8, then you have the delay associated with pushing this video stream from JSC to Las Vegas, and finally the decoder delay associated with actually displaying the video.
On the way back, you have the VoIP audio feed from Las Vegas that travels back to JSC, then to White Sands, then back up to ISS via TDRS.
The delay you see is the sum of all of those.
4K video is a lot of data to push through a satellite link that was put into place long before 4K video was ever a thing. The second video is "only" HD, which I would suspect suffers less of a codec delay.
That said, here's a better explanation of why the delay is less apparent in the second video:
The second video doesn't require round-trip communication from space to ground to be real-time to keep the music in sync.
Timing issues like that are actually very similar to what marching bands and drum corps have to deal with all the time. The solution is pretty simple: the most delayed member of the ensemble (Chris Hadfield in this instance, or the farthest backfield members of the marching group) are the timing sources, and everyone else just plays with what they hear. I suspect there was also a click track on BNL's in-ear monitors to help.
If you were to see a recording of this from Chris Hadfield's perspective, it would have sounded horribly out of sync (again, just like in marching band and drum corps).
I also suspect this was produced from multiple takes, which would cover any other ensemble tears there may have been.