Why are some coils coated and some not?

To aid safety and to prevent heat losses

Induction coils are coated for two reasons. First is safety from accidental contact by operators and machinery. Second is to prevent the loss of heat from the hot part due to radiation, and convection. These types of coating are typically of the form of epoxy coatings, ceramic coatings, or any non-metallic coatings like silica sleeves or higher temperature alumina sleeves.