Allow me to explain:
As others have said, 'gain' is the word that has been around in audio since the beginning, and it is the same thing as 'volume'.
All amps preamplify a signal. A guitar signal is very, very quiet. The preamplifier raises the volume to the level where the amp can do its work in EQ, etc., sending the right volume to the output stage of the amplifier. The small tubes in your amp, the 12AX7s, are your preamp tubes. The four larger tubes are the power amp tubes, and there's also a Rectifier tube that can be switched in, or you can use a solid state rectifier that's built into the amp depending on how quickly you want the power tubes to act on the signal. The tube rectifier slows the initial note attack down a little bit.
The Presence control acts on the amplification section adding or reducing negative feedback to make the signal brighter or less bright in a different frequency area than the Treble control or the bright switch (if there is one).
A boost pedal is simply a volume control. It amplifies the signal BEFORE the signal hits the preamp; therefore it operates on V1, the preamplifier tube that provides much of the gain to the parts of the preamp that follow it. A boost pedal distorts V1 and therefore, the tubes that follow it.
A Mesa uses 'cascading gain' to make one stage of amplification hit another stage of amplification adding distortion to the signal.
On the Lone Star, the clean gain control distorts less because the amp is set up to distort less in its range of operation. The Lead gain control operates to distort the preamp far more quickly.
In the lead channel, the drive knob simply adds another tube distortion stage to the signal over and above the gain control. Simple as that. There are several choices regarding how much more gain you want to add. You can add this to Channel two by moving the switch that chooses it to the left.
Once you do that, the switch below it allows you to select different ranges of gain, and the drive knob allows you to control those stages.
None of the drive controls affect the clean channel.
The channel 'masters' on the Lone Star are there to:
a. Balance the level of the channels whether or not using the global master volume on the right of the amp's panel; and/or
b. Every volume control adds another layer of amplification to a signal. The Lone Star gives you the option to bypass the amp's global Master and effects loop for a signal with fewer gain stages. I run my Lone Star this way because I don't need tons of gain for my style of music, and I don't use effects loops. I like running my effects into the front of the amp where the gain stages in the preamp affect them. There's no right or wrong ti this, it's just how I roll.
All you're doing when adding gain is, as others have said, adding volume to the next stage, or in the case of master volume, to the output tubes.
So here's what's happening with gain, and multiple gain stages:
As you add gain to a tube, it begins to 'clip'. 'Clipping' describes the top of a tube's sine wave becoming squared off, eventually becoming a square wave. What's that? A fuzz box does the very same thing; converts a sine wave to a square wave.
When you turn the gain up on a tube amplifier, the signal becomes more compressed - meaning, there's less dynamic range (dynamic range can be thought of as the difference between how loud and how soft a signal is).
Compression is desired when you want a signal to sustain ('sing') more - that's because compression increases the amount of time it takes for a note to decay. It does this because as dynamic range is decreased, soft signals that are compressed become louder in addition to loud signals becoming less loud. It's not much different than how a studio compressor works - it's merely akin to an automatic volume control.
So jazzers want a note to decay quickly and sound more acoustic; they prefer clean amps, often solid state amps. Rock players often want a note to carry and sustain longer, so for players desiring that, compression is good.
Country players like compression before the signal hits an amp because they can pick hard and clean at gig volume without blowing an audience's ears out, or soft and still be heard. Pedals are usually used to achieve this.
Increasing the gain to clipping also reduces high frequencies in the signal itself, and increases the relative amount of bass. However, a distorted tube adds its own high frequency harmonics to the fundamental signal. This is why, once the gain is up, electric guitars start to sound more like the amplifier they're driving and less like the acoustic instruments they're similar to.
What are harmonics? They're the overtones that allow you to distinguish, say, a flute from a guitar playing the same note. That's the main reason why instruments sound different from one another, though there are also other reasons, such as what happens at the attack of a note. There's a ton of information about harmonics on the web if you care to delve further into all this.
One last thing: A tube amplifier runs at around 10% or more distortion of the signal even when it's supposedly 'clean'.This distortion colors the signal.
By way of contrast, a typical hi-fi amplifier runs at less than 1% distortion even with a loud signal. This is why a clean guitar amp sounds different from running your guitar into a hi fi amp (or recording console). The more you drive the tubes, the more distortion you add to the signal, thus coloring it more.
I hope this helps.
My Lone Star is the tan amp close to the middle between the rack and the black cabinet in this pic; I've had it for about ten years. They're great amps.