Good summary.
Detailing clay works somewhat like sandpaper in that there is an abrasive in the clay that when rubbed over the surface using a lubricant the abrasives will basically sand off the tops of anything bonded or sticking-up on the surface of the paint. As the above surface bonded contaminants are removed the surface will become flat or smooth and at this point the clay stops abrading and simply glides over the surface. At this point you wipe off the residue and move on to new territory.
Because the clay is tacky, as the contaminant are removed they accumulate into the clay, for this reason you need to knead your clay to expose a fresh surface and at some point the clay will become so loaded with contaminants that you'll want to dispose of it and next time you clay start with fresh clay.
The less aggressive the clay, the more passes or strokes it will require to abrade off any bonded contaminants, that said the very aggressive clays are aggressive enough that on some paint systems they will cause what's referred to as clay haze, which is another way of saying clay scratches. Aggressive clays are typically for Professional Detailers and technicians that work in body shops where speed is king and because after the claying process the paint is usually going to be buffed with a rotary buffer so any haze the aggressive clay instill will be obliterated by the buffing step with the rotary buffer.
I've used aggressive clay and hazed the paint on a couple of cars in the past and in once case a PC with a SMR was powerful enough to remove the hazing and in another instance, a Mercedes-Benz trunk lid, the paint was so hard that it required a rotary buffer with a wool pad and an aggressive compound to remove the hazing. How hard it is to remove a defect out of any car has nothing to do with the clay but instead has everything to do with the hardness or polishability of the paint in question and this is a huge variable that you just don't know until you bring your hand or your polisher down onto the paint surface and do a little testing.
As long as you stick with the ultra fine, fine and medium grade clays you won't have any problems. Keep in mind just as important as using the right product for the job is to always work clean, that is everything must be clean before claying or any paint care procedure. So wash, rinse and dry the car thoroughly before claying and you'll be okay.