Hmmm...Claying isn't at all an abrasive process. It more of a "Pressure" dynamic.
You are trying to squeeze out anything that lies between the clear coat and the clay. If you squeeze without lubrication you are likely to marr.
Its sort of like an ice skate. The heat of the blade melts the ice below the blade and the skate glides across the ice.
If ice weren't "slippery" then it would be like skating on sand. Not gonna work.
Using the softer green clay will clear off anything that lies on top of the wax.
Using the harder yellow/red/blue/grey/white clay clears off anything that lies above the clear coat.
Claying is the best thing you can do for your paint. I'll take clay over a wax or polish any day. The guy who started the Autopia site says today's clear coats have made most waxes obsolete. A good once over with Clay and the shine is restored. 90% of what is removed from Claying is pollution, if you live near an airport and have never clayed you would need a few bars. The polutants in the air are what cloud the clarity of the clear coat. Not really so much the sediments from the road and the stones from surrounding landscape. You ALWAYS want to clay before applying any wax, rubbing on the paint will dislodge the micro sediments that didn't come off in the wash and will give your wax applicator a nice sand paper dynamic
Now swirls are another matter. And I'm of the opinino that your chamois is no friend. The Chamois squeaks which is NO GOOD. Absorbers and Chamois should only be used on the canvas top and glass, no paint. When you hear that squeaking you can bet there is some micro marring going on. Maybe not so noticeable but over time it builds up. For drying you should be blotting as little as possible with as small a section of waffle weave as possible.
As far as the differences between polishes and waxes etc. here are their purposes and they should be used in this order
1. Swirl Remover (rounds the edges, Poorboys SSR line)
2. Polish (deep cleans the paint, Klasse AIO, Zaino, Werkstatt Prime, Menzerma)
3. Sealant (encapsulates the clear coat from the elements, involves curing time Werkstatt Trigger, Menzerma FMJ, Zaino, Poorboys EXP)
4. wax: carnauba or synthetic (dresses the paint, no protection P21s,S100, Nattys Blue, FK Pink Wax, FK 1000P, Zaino)
5. anti static topper (FK 425 can't think of another due to patents)
The meguiars NXT combines many of the above in one step. Cleans, Shines and protects. That's why I don't use it on paint, I like to control each stage with my preferred product rather than trying to do it all at once. But its very good at hiding swirls on dark paint. Great at protecting wheels too. But I personally wouldn't use it regularly due to its cleaning properties, if it has abrasives skip it.
if you want a boost in the shine but don't want to break out the wax try using a spray wax like Duragloss Aqua Wax, Optimum Car Wax or Zaino Z8 (Zaino is a bit finicky about what its used over so if you go Zaino you need to go all the way).
The other two mentioned are top notch as well and get along well and are cheap. I would top those with FK 425, I didn't do this once only to find a thin film of soot on my paint the next morning. When you apply the 425 and feel the paint you'll know what I'm talking about, its like teflon.