I'm no expert or professional detailer but paint correction is actually a bit of a misnomer. It's more accurately clear coat correction.

There are times when the clear coat over a car's paint is not uniform or smooth eg uneven respray of clear coat by a body shop after a car accident leading to a phenomenon known as orange peel. Other times, a improperly done car wash with inadequate lubricants or the wrong types of cloths/sponges leads to superficial abrasions to the clear coat known as swirls. Deeper damage from car keys will lead to scratches. Rainwater or tap water with high mineral content if allowed to dry on the clear coat will leave behind mineral deposits on the clear coat known as water spots. Finally debris from the roads and iron containing brake dust from the car's own brake pads can deposit on the clear coat as embedded tar and iron deposits.

In summary these are the things that cause the clear coat to lose its original gloss and shine : superficial dirt, embedded tar and iron deposits, orange peel, swirls, water spots and deep scratches.

There are a few levels of car detailing :

Maintenance car wash with simple car shampoo that removes the loose dirt on the clear coat.

Decontamination car wash with chemical decontaminants like dedicated iron removers and tar removers in addition to the car shampoo.

Physical decontamination by rubbing a clay bar or clay mitt over the clear coat to further remove the tar and embedded particles. Note that ironically, claying the clear coat is v effective at removing bonded and embedded dirt and tar but it by itself is an abrasive process and will introduce more swirls into the clear coat.

Finally you have paint correction or known to the general public as polishing(mild), compounding(more drastic) and wet sanding(most drastic). These processes serve to make the clear coat more uniform/smooth by removing the most superficial layer of clear coat thus removing the abrasions(swirls), water marks and scratches on the surface of the clear coat. By definition, paint correction always leads to a thinner layer of clear coat as it is a subtractive procedure and a car's clear coat has only a finite number of paint corrections in its lifetime before you finally hit bare paint. All the above processes does not strictly protect the clear coat but merely gives it a uniform surface.

The next step is to protect the clear coat by applying a sacrificial physical barrier separating the elements from the clear coat. They are waxes(usually naturally occurring like carnauba, short term protection), sealants(usually artificial polymers, intermediate term) and finally ceramic coatings, which are actually SiO2 or essentially liquid sand. Ceramic coating acts like an extra layer of clear coat and gives the longest lasting and most effective form of protection over clear coat.

The most drastic form of protection is applying a special plastic film over the car surface known as Paint Protective Film PPF. That is what clear bras are.