Fact is, both situations can cause a cupped appearance.
: Take a normal, kiln-dried to 8%, solid hardwood floor and install that over a very damp crawl space where the subfloor reads 16%+ MC and that floor will cup. The cupping will be caused by the bottom of the boards getting wetter (higher MC) than the surface. This is the typical scenario in a cupped floor appearance.
: Take a normal, kiln dried to 8%, solid wood floor and install it properly over a subfloor that is within specs, say, 10% MC. The crawl space is dry and there are no dampness issues in the crawl space. The normal RH is typically inside the home is 45% on average. Now, the owners go away for a few months in the summer and turn off the HVAC. They also live in an area where the outside humidity gets pretty high in the summer and 80+ RH outside is the average in their area. They also have some very large skylights. For the sake of argument, during their vacation, the interior RH goes up to 80%+ and stays there for most of the time they're away (greenhouse effect). Now the floors were tight and fine at 45% RH but at 80%+RH, they're picking up some moisture and expanding. Since they are well nailed (as they should be), there is no where else to go but up. And that's what happens. As the boards expand in width, they "compress" against each other, crushing the wood fibers and cellular structure permanently and forcing the edges up in a cupped appearance. The biggest difference in appearance is compression set floors will had a dramatic upturn right at the seams between the boards where the middle will appear relatively flat and the edges will be very peaked. A floor cupped from moisture from below will have a more uniform concave appearance (more like a bowl) and may even have some small gaps at the seams.
Does a floor have to cup to compress? Does it compress first or later after it compresses?
Compression set is a result of the expansion of the floor boards due to taking on moisture, regardless of where the moisture came from. And generally, a floor will appear "cupped" if compression set is evident.