In regards to Hyundai headlamps, there appears to be a softer/more rubbery, ding-resistant plastic coating over the underlying plastic. However this doesn't seem to hold up to sunlight. On my 4.5 year old elantra, the coating fogged and yellowed, then began wearing away. If you polish (say with plastX), you'll end up with nice clear covers where the coating has worn off, and an ugly hazy film where it hasn't.
I ended up wetsanding this coating off the rest of the way with 1500 grit. Once you get going you will be able to tell where the coating remains while rinsing and concentrate on those areas with finger pressure. The coating does not show as much of a milky sanded finish as the rest of the lens, and will appear to be darker colored while sanding and rinsing. This coating does sand off with 1500 grit no problem.
Once it was all gone, sanding everywhere to see that it is, I went to 2000 grit, then plast-x.
I found the plast-x didn't quite cut 2000 grit easily enough so I used some sort of "heavy scratch remover for plastic" polish I had laying around from a 3-step kit who's name escapes me, then plast-x finished up just fine with a couple applications.
In my opinion you need some sort of intermediate step inbetween 2000 grit and plast-x if you're doing this by hand.