It's more likely they simply have multiple versions made by multiple companies.
I used to work on the Pioneer Karaoke when it first came out on 12" laser disk [late 80s]
They very definitely made only one video per song, & went to great pains to ensure the time-code matched, video to audio.
No doubt it's a much simpler process these days - we couldn't record all this stuff on a laptop, it was all on analog tape, right til the last minute when it was transcoded to digital for the disc, but I'm still not sure it would be economically viable to produce multiple videos for a single song.
The videos cost considerably more to make than the music - which is why most karaoke these days just uses CD+G with lyrics & no video at all.
The only karaoke I see these days with video seems to be Russian - a market I know nothing about, so perhaps they do things differently there, but I still doubt it.