Well, stomp compression is a process (as opposed to an effect), much like applying a plugin or outboard compressor to a signal.
I don't know what's going on under-the-hood with Amp Compression, but logic tells me it's not quite the same thing. I've read here previously that it doesn't do what we're talking about here 'though, so I checked the manual:
This “Compressor” parameter is different from the Compressor effect, as it is a part of the simulated amp circuit. In other words, it allows for completely different sounds compared to compressors that are inserted before (pre) or after (post) the amp module. Distorted signals are not affected by compression; so only clean signals will be boosted. The dynamics of your playing are fully retained, allowing you to go from a crunchy sound to a compressed, clean sound, purely by the strength of your picking. The volume knob on your guitar works exactly as you would expect: for instance, reducing the volume of your guitar will transform a dynamic crunch into a clean, compressed sound with full energy.
Somehow 'though, when I crank it up using driven tones it gives me a "creamier" playing response - a smoother, seemingly-more-sustaining result. IDK why I have this impression given that the manual implies this should only be apparent using clean sounds, but hey, I love it.
cheers Nicky - converted...