First, I want to thank you for asking this question, as many folks out thre wonder what the differences are with glaze's, cutting compounds, waxes and resin putty with todays and yesterdays paints.
This is my opinion and my expierence only, and as we know, opinions vary and so do expierences.
Yesterdays technology of paint, for me as I am of the baby boomer generation, will remember that painting a vehicle used to be a one stage paint, be it either a laquer paint or enamal. You would prep the body, and paint it, once, maybe laying down several coats depending on you wallet. The factories have it down to a science so that they use the minimum amount to satisfy the car and customer.
With the discovey of the two stage process, base coat and clear coat. We have found that they are more durable and easier to repair and match up. Now to get down to the brass knuckles of your questions.
When a vehicle is freshly painted with either a one stage or 2 stage paint, after it sets up for a couple days, you would need to smooth out the fresh paint, and you may do this by 1 color sanding which will entail cut, buff & glaze, or 2 just cut, buff & glaze.
Now, explantion of cut. Cut will take down the paint, kind of a liquid sand paper for lack of a better term. Then the second stage is buff. you need to polish out the paint after the liquid sand paper. Just a finer step. Then glaze. as you do not want to use any waxe's, on the fresh paint to allow the paint to cure and shrink. Glaze's do not have any wax in them, they are supposed to be a chemical clean, not a abrassive cleaning.
You would have to allow the paint time to cure. The painters and body shops like to allow at least 30 to 90 days for the paint to "cure". While cureing if going for a "show appearence" or daily driver what happens is that the paint may shrink in some areas of the paint job, thus allowing the painter to do some color sanding, cut and buff for a final until it is time to seal the pours of the paint.
To maintain that cleanliness on the paint, we use a good glaze, no sealers whatsoever.
Also when a car is freshly painted, you would have a good idea how much paint is on the vehicle, that you have to work with.
Older cars have may have a thin paint, and if they have changed owners several times, you will not be aware of how much paint is on you vehicle, and if using a "cut" may burn through the paint, unable to put that back with out painting the car entirely.
Now, with light oxidation, I prefer the clay bar to a cut, as the clay will just take off any contamination on the paint and not the paint itself. Then by using a good carnauba wax, this will finish the job by clearing up the "cloud" that oxidation presents itself to be. thus leaving you with as much paint on your vehicle and lengthing out the life of the paint.
This may be kind of a lengthly article, but I hope it answers you questions about the difference's and why glaze or clay.
On my show cars, I always clean them with our Cal. Clear Coat Hand Glaze, before a show as it is like putting a volume knob on my paint and turning it UP!
Good luck, keep th questions comming!