I wrote this reply on The Corvette Forum to answer a question regarding why a clay is necessary before polishing. I hope it helps in this discussion.
Wet sanding and a clay bar work in very similar fashion, but I would argue that a liquid, such as a polish, works very differently because of the action of each.
Both a clay bar and sandpaper work well at 'leveling' or 'flattening' the paint because of their firmness. The firmness does a much more effective job at removing just the high points of the paint, whether it be above surface contamination or orange peel.
So am I telling you that a clay bar can remove orange peel? Yes, although to a very minor degree. I have, on many occasions, used a very aggressive clay bar to remove surface contamination, and the end result was a surface where the top of the orange peel was dulled. This proves the paint was abraded by the clay, and the majority of the pressure and paint removal was focused on the high points of the paint. This is of course an extreme example.
Firmness is so important that Trizact Sanding discs change their grit level depending on the firmness of the backing. By focusing the action on just the high points, the cutting action is theoretically increased. It is easy to remove the high points of orange peel, it is very difficult to get paint completely flat, because as you approach 'flat', more stiffness is needed to keep the sand paper for contouring the more gradual changes in elevation and the surface area increase dramatically.
A piece of 'bonded' contamination sticks above the paint and represents a dramatic high point. As clay 'floats' above the surface, the majority of it's cutting action is focused solely on that 'bump'. This is what allows the clay to effectively remove the contamination but still be relativity safe when it's force is equally distributed across paint. This is why clay can be abrasive enough to remove surface contamination while not overly abrading the paint.
As far as clay being interchangeable with sandpaper, to some degree it is, although the grit levels would be much different. I know of some detailers who, instead of claying a car, will wet sand it quickly with 4000-6000 grit, felt backed (semi firm), sandpaper on severely contaminated cars. They feel that this approach (since an abrasive clay would be needed that would severly mar the paint) is they feel they have better control with the sand paper and get less marring.
Another myth is that clay will 'pull' the contamination into the clay, protecting it from marring the paint. This, of course, isn't true. While it is possible that large pieces of contamination may be removed completely, they usually end up marring the paint, and leaving little hair line scratches. As clay is worked over a piece of 'stubborn' contamination, it is abraded off very gently. You can see this happen, as the piece of contamination seems to shrink each time the clay passes over the area. Usually the removed is ground so fine as it is abraded away, that it presents no real danger to the paint, until the clay bar's surface becomes overly contaminated, at which point it can start to mar paint.
When you polish paint with a machine, you are applying a liquid suspension, with a foam or soft pile wool pad. Unless extreme RPM's are used, and the centripetal force pulls the pad (particularly a wool pad) outward making it tauter, the entire polishing action is focused over a very broad area. While the bump of contamination will still present an area of increased force, it is repetitively small in comparison.
So the action of the machine will act to abrade away the bump with slightly more force then the rest of the surface area, but the because machine polishing will contor readily to the surfaces, the area is abraded with only more measurable force then the surrounding area. If the hardness of the contamination is as hard as the paint and 'stuck' enough to prevent sheering off (which presents another problem) the removal of the contaminant will reduce slightly faster then the surrounding paint being polished.
I have polished rough, contaminated sections of paint before, and it still felt rough and contaminated after polishing. Even fairly aggressive polishing didn't make the surface completely smooth. By the same token, a clay bar and 20 seconds removed the gritty texture.
I have also fairly aggressively polished areas and found little pieces of rail dust still attached to the paint (this was my wife's cars, which gets a lot of rail dust on the rear bumper).
Before detailer's clay was invented, body shops (some still do) used to polish off over spray with a buffer. Usually this was/is done by using a high speed rotary at high RPM with a wool pad. Think of a wool pad like a weed whacker: At low RPM the weed whacker's line can't even cut grass. However if the RPM is increased, the centripetal force pulls the string taut, and now the string has great leveling power. A wool pad at high RPM is fairly efficient (in polishing terms) at leveling, particularly in the outer 1/3 of the pad (where the force is the greatest).
Detailer's clay was developed in Japan with the goal of removing over spray quicker and more efficiently
The other question I believe that was asked is what benefit does claying have before polishing?
I believe that polishing on a completely clean and free surface is the best way to insure optimal results. During the polishing process, the majority of the abrasives have to move or roll around between the paint and the pad. Ideally this would happen in a consistent manner However contamination, and even paint that has been removed during the polishing process, can cause less then ideal performance as the abrasives become coated, attached to the pad, or clumped together, all of which will negatively affect the results. (This is a very broad generalization)
Obviously on severly contaminated paint, this is going to be more of an issue, and it is not uncommon for pad's to 'gum up' much faster. This is of course is assuming that the contaminants are relativity non-abrasive and don't scour the paint excessively themselves. However if the containment is particularly hard and not 'stuck' well to the paint, it could dislodge and become trapped into a pore of the pad, which could cause swirling during the polishing process.
So why hasn't this been your experience? I'm going to guess that in most cases the car's you have polished have been in relativity good shape (do to your own care) and have never really been severly contaminated. If you care for your car frequently and wash it often, there is a very good chance that the contamination never becomes so severe that polishing will not remove it, nor will it severly impact polishing performance. On more neglected finishes the difference, IME, becomes more apparent.
Well I have rambled, and I really don't have the energy to proof read it tonight, so I'm not even sure if my explanation makes any sense, but I will look over it tomorrow and clean it up if I have the chance (Super Run On Sentence)