I’m not sure what you mean by the amp breaking up, but I guess you mean reaching saturation?
I’ll try to give you a quick run down of how such amplifiers work. Essentially amplifying is a bit of a problem: You have some sort of electric signal (time dependent) and increase the voltage and the power, usually by some time independent voltage.
An early way of getting this done were triode vacuum tubes. This uses an effect where a light bulb will emit electrons in use. This is paired with a grid, which will electrostatically absorb some of the electrons depending on voltage. And suddenly you have a quite crude amplifier (later this was superseded by the much superior technology of transistors).
Now clearly this technology is not perfect. The tube can only emit electrons, not take them in (so it is asymmetric), and if you put in a higher voltage the output will not be equally much higher (non linear).
This means that this amplification will change the waveform (distortion). In a HiFi-amplifier you’d use multiple stages with negative feedback loops to make this more linear, in a guitar amplifier this is what you want!
Now, the problem is that this distortion depends on the amplitude, so a small signal will distort less than a big one. The way to amend this is to attenuate this before the actual amplifier (gain). This can then adapt the signal so you can drive the amp less hard. Due to compression turning up the gain will partially increase volume, partially color.
Now, let’s say we have an active instrument (already with a built in amp) the signal might be too strong. Then we might attenuate the signal. This is what the two inputs are for.
After going through the (pre)amp and optionally an effects section the signal will go through a power amp, which drives the speaker.
Usually you do have another knob here, which is the volume knob.
Technically gain specifies the factor by which a signal is amplified. In these contexts this is is usually a pot that sends part of the signal to ground. These can sit in different positions in the signal chain, and this will have different effects on the sound, and different vendors use different names.
But generally you have some something like this:
Input → attenuate (gain) → preamp → attenuate (volume) → power amp → speaker
You’d use the attenuated input if the attenuation of gain all the way down is not sufficient for a clean signal.
(Sometimes you’d get an additional amp before the preamp to drive the preamp harder, often called drive).
The guitar volume knob will act the same as a gain knob, just at a different section in the signal chain: It cuts away some of the signal.
As far as I understand the Volume knob on your amp acts as ”gain“, so there is no way to attenuate the signal after the preamp section.
Now if we ignore frequency dependent stuff (the guitar volume knob’s effect will depend on frequency) each knob will cut away a certain factor of the signal. And assuming that the signal path to the preamp is sufficiently linear you’d expect a total (logarithmic) gain at the preamp of
g_guitar + g_input + g_volume
Now the problem is that the positions on the knobs are only labels. What matters is the resistance curve of the potentiometer under the knob. Since perceived loudness is logarithmic pots for audio tend to be so called ”logarithmic“ pots, thats is, the resistance curve is (in theory) exponential of the angle. While no pot is perfect in this case this would mean the log gain of guitar and volume knob are proportional to their angle. So you can probably say ”An adjustment of the guitar knob by x degrees is like adjusting the amp knob by y degrees, and using the attenuated input is like adjusting the amp knob by z degrees.
But the exact values will depend on the individual pots. Now in practice the guitar knob also has a frequency dependent effect and will be affected by every non-linearity in the signal path. The attenuated input gain will be affected by any non-linearity between the attenuation and the preamp. So these will affect the tone in slightly different ways.
So now addressing your scenarios:
- If you use the attenuated input a smaller signal will reach the preamp, so you get less distortion. To get more or less the same distortion you will need to reduce the attenuation of the volume knob. The distortion of the amp more or less depends on the volume that comes in, so it should distort more or less at the same loudness (although as I said this does also depend on other non-linearities in the path, and where exactly the voltage dividers sit).
- Same as 1, but the change of signal directly at the guitar affects more stuff, so you will hear a noticeable change of tone (loss of high frequencies), especially on a passive instrument.
Generally also one thing to keep in mind is that the longer a signal path is the more noise there will be. So if you have a strong signal and attenuate at the end you will have much less noise than otherwise. This means that using the guitar knob is nice for quick, interactive control, but you should try to keep it on the open side. Choose the input so that you can use as much of the range the amp gives you (if your distortion is unusable at 5 half of that knob is unusable, but it gets harder to fine tune as your scale is now 0 to 5). Then choose your amp gain so that you get the most distortion you want with guitar pot fully open. Then you can fine adjust on the guitar.
