Okay, I will take a deep breath here. I think what is making you confused is the voltage ratings. In Perry's diagrams (and on many amps) the potentiometer is labeled with voltages. Those voltage ratings (as Perry describes, if you read it correctly) are the input voltages needed to amplify the signal to a currect strong enough to match the rating of the amp. if you give the amp too much potential, you may fry it even if you have the gain set all the way down. if you don't give the amp enough potential, it will not exceed its rated power and the output would be highly clipped.
There is no magic behind this. The gain control knob is there because not all head units send out the same voltage. Also, it gives the user the option to make his/her music quieter than its ratings. There is very little difference in theory in the function of the potentiometer on your amplifier versus the function of the potentiometer of your boom box or whatever actively powered system that has a "volume" knob. potentiometers are placed before relevant amplification, some after (or even both. when i used to play guitar, i had an amp that had a "pre" gain and "post" gain in case you wanted peripheral effects).
And I'm sorry that webpage didn't have credentials, I should have thought of that. But basically what I was trying to get across was that explanations of "there is no difference" are far thoroughly explained than anything I have found claiming that there is some magical property in the potentiometers of car audio amps that make them a higher deity than lowly volume knobs.
Gain - Wikipedia, the free encyclopedia
whenever i see somebody say "make sure a professional sets your gains for you" i just laugh to myself.
and yes, for those who ask "umadbro?", yes. i'm mad.