same amps, different supply voltages. Equal volume?

[Hybrid fourdoor]

Let me see if I understand how this works. Say we have two amps, same design, both at 20x gain. But one has a 12V supply (amp1) and the other 24V (amp2).

Does an amp work by taking the input voltage and mulitplying it by the gain? Say a signal of 0.2V comes in, the amp ups that signal to 4V, so both are still good. But lets say we got to 0.5V input, now up to 10V, so now amp1 starts clipping because its nearing its supply (maximum) voltage, but the other amp keeps going fine because its only halfway.

So until the first one clips, they will play at the same volume right (with the same input signal)?

Thanks.

[till]

yes