For the last few months I have been playing electric guitar on a small 5W tube amp with a nice saturated gain channel. This past weekend I picked up a Big Muff Pi pedal, which I believe is classified as distortion.
In having played the amp alone, on the gain channel, I get a nice swirling distortion. Now, playing the pedal through the clean channel, I notice a couple of things. The distortion is nice. It's fuzzier, a quality I couldn't get with the amp. But I also notice that the distortion itself does not have a variable quality. It seems that the sound has a singular quality, whereas the amp distortion was swirling and would come and go slightly.
What are the physics for these two distortion approaches? Since I named the pedal I will share that the amp is a Marshall 5W tube combo (without reverb).
EDIT: I want to be clear. I am not concerned about whether this pedal is classified among those in the know as a fuzz pedal. At the end of the day, both the amp and the pedal are distorting the signal.
My question is about the physics of why it appears to be different in each case, specifically swirling (in the amp) and a very straight-ahead sound (the pedal)