Tubes (and transistor) are active component, depending on circuit values have a GAIN (20 to 60:1 in a typical tube amp). Let's 20:1 the gain of each stage of a 12AX7. A signal of 1 volt get out of stage 1 at 20v, into stage2, out at 400v. The power supply is, say, 200v. So the second stage CLIP AND SATURATE.
Pots are passive component, a voltage divider, than can varies output v from input value down to 0. If we put the a pot between 2 stages, label it gain, put if halfway, the second stage will have 10v input 200v out, at the verge of breakup.
Well, it's not that simple, but it gives you an idea! Tubes are complex, component are not ideal: after about 100 years of amp tech knowledge evolution, tube amps nowadays use each imperfection to reach a desired behavior (compression, sag, clipping, saturation, brightness, ...). Digital tech is a lot younger, and can copy those imperfections in lots of different ways. I hope we will be able, in the digital domain, to mix those imperfection to ours artistic needs (like fizz).