Gearhead wrote:
Gain is voltage increase whereas volume is what comes out of your speakers.
+1. I was taught never to use the word "volume" unless I was talking about dB SPL - and even then, rather to use dB SPL. But in a guitar amp, there are different naming conventions that guitarists understand, although they are not, strictly speaking, correct. Like "Vibrato" (which is actually tremolo).
So "Gain" is usually the amount of overdrive from the preamp valves, while "Volume" is how loud it is. Note that at lower gain settings, the gain will also affect the volume and at higher volumes an amp's power amp will distort too, so there is a lot of interraction.
Vintage and many vintage-style amps just have a volume (which is actually gain) and you have to turn up to get the amp to drive. More modern amps may have gain and volume per channel and then even a "master volume" controlling the overall volume too.