Looks like oxidation to me. I would personally have them wetsanded with a couple layers of UV-resistant clear coat applied afterwards.

 

Agree with above, you can also look into clear bra-ing the headlights after they are restored. I did mine restoration but it came back after a year even after applying UV, restored it again and same thing after another year, someone introduced me to Xpel clear bra, restored it again and clear bra'd and hasn't yellowed in 2 years since I had it.

Edit: also, looks like your car does have some sort of clear bra on the fender/hood

 

Definitely Oxidation, look at your rubber seal next to the hood... it's deteriorated. The only reason your paint doesn't look equally as bad there is because of the clear bra that looks to be on it. The good news is that it's not that bad. A orbital polisher, some compound and polish, then finishing off with wax will make it look like new!

 

They don't look bad enough to wet sand and polish. If you do, prepare to do it once a year afterwards or they will look worst than they do now.

 

Yeah that looks like oxidation, typically headlights start their oxidation process from the top like (at least from my experience).