Paint correction can involve machine polishing varying cleanser, polish, or compound grades. (can also be done by hand, but in today’s time and with today’s finishing, I would suggest machine polishing, preferably via an orbital polisher) Paint correction needs a high degree of skill and concentration but is done properly, and it really can change the look of a car by dealing with hard water marks, etching caused by bird droppings or bug and tar, swirl marks, scratches, and fading or dull paint.
Done professionally, paint correction is entirely safe and will not cause any issues for your paint.