It all has to do with clipping, and the nature of the distortion that is produced when you clip. And BrianG is right to ask if the preamp is digital. The tube portion, which is the 1st and likely 2nd stage is analog; thereafter the processor is digital.
Tubes (and you gotta remember the crowd that really believes in these are a tad, should I say, "culty", whether the hi-fi crowd, or the guitar amp crowd) supposedly produce dominantly even-order harmonics, as opposed to odd-order harmonics, when you overdrive (clip) them. This makes for a smoother, controlled, more mellow (not "grainy" or harsh) sound quality. (I must confess, I have a McIntosh MA-230 at home, that I recently refurbish, now that the Russians are making 7591A's again, and it sounds SUPERB! Rated 30 watts a channel, it tests at 50+, and if I put out my old pair of EV 12TRX's during one of my cookouts, neighbors become pretty well acquainted with my musical tastes, which sorta runs towards non-commercial rock, blues, and whack (Zappa).
Typical tubes used for preamp, whether guitar or hi-fi, are the famous 12AX7, although you do see some 12AT7's around. Normally these are used in the classic "push-pull" arrangement, where the positive and negative portions of the waveform amplified by different stages of the tube.
After the preamp, where this overdrive can take place (or not depending on your settings, and the preamp's design: Blues guitar amps have less overdrive available), the digital processing takes place, which is where the "whah-whah" and 57,000 other settings are available.
You can get guitar preamp processors, for not a lot of dough (maybe 300-400 USD), with tube preamps in them, and then send this signal to a nice power amp (Crown, QSC, or whatever is available locally), which is the way it is often done, again, for less $$$. The all in one units are convenient, packaging-wise, but you gotta pay.
BK