Afaict these aren't related.
This is one part of 2000s tech I'm happy to have mostly forgotten about.
DivX the video codec started out as an unlicensed hacked version of Microsoft’s MPEG-4 v3 codec binary. Since it wasn’t a commercial product and was legally dubious, the author called it DivX ;-) with the smiley in the name.
When it became unexpectedly popular during the dot-com boom time, someone of course set up a DivX company that dropped the smiley, eventually rewrote the codec, and presumably acquired the trademark from the defunct DIVX (or just took it over if the registration expired, I don’t know).
and then, iirc, this is where xvid come into being. I think it was the same codec just re-written and given back to the opensource world, hence the reason for naming it "divx" spelled backwards.
You could encode a CD sized video file, burn it, and watch it.