The gain stage starts by amplifying the signal by, roughly, factors between 10 and 100, and then it gets mangled down to a clipped signal on the way out. ...
(snippety-snip)
there's a little thing in the clipping circuit that softens this edge it's a small capacitor, which you could look at as a sort of 'holding cell' for charge, and what it does is smooth the sound out with its charge-storing goodness... it's like when little kids in art class rub over a crayon/pencil drawing with a tissue to smooth out the rough edges. As the drive knob gets turned up more, this effect becomes more pronounced, so while there is definitely more clipping going on with the drive knob the softening is going on more, so it doesn't seem like it's been cranked as much as it has been if you're listening for 'buzz' - but there's more compression than you'd think there would be.