Hello so I have some basic questions about the things above and how they work.

Almost all famous guitarist use tube amps, saying they love how the natural tube distortion tone makes them closer too that tone they were always searching for.
Why do they use distortion pedals if they already have their custom made amps have a distortion channel already?

I've seen Joe Satriani click onto his distortion pedal and he started to play clean. That means he wasn't using the distortion channel on his amp.
And not just him, many guitarist do that as well.

I myself use the amp distortion, just because.

Are guitarist using tube amps just for the amazing clean sound so that they can beef it up with gain with pedals?
Stomp boxes just drive the tubes in the amp harder, so you get dirt from a clean channel or take a diirty channel over the top. BTW, some stomp pedals have tubes, too.

Another reason for pedals is to control the type of distortion...a little overdrive, some fuzz, all out distortion, etc.
Maybe it was a proprietary footswitch for the amp?

If not, as jetwash said, it's not uncommon to see players getting sick tones from driving some OD into a clean channel!
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i think in general (completely my opinion) when talking about amps people are talking about the base sound. The base characteristics of the sound generated by either tube or solid state before any manipulation. The pedals are used to manipulate or enhance the sound to shape it how the artist wants. So when talking about Tube or solidstate it is the base sound they are referring too.
I am of the opinion that the same rings true when talking about the wood used in the guitar bodies. I know they have different properties and different sound but i could not distinguish the difference. The specific nuances to me are just part of a bigger package... pickups, wood used, etc. Please don't flame me, i am not saying that the woods used don't make a difference, i am saying i can't distinguish.
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Every guitar and bass forum I've visited has some people chasing some magical tone that will shoot jizzing unicorns riding on a rainbow out of their amp.
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Maybe it was a proprietary footswitch for the amp?

+1. He was probably just changing channels on his amp.
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Satch has said in the past that he likes to run pedals through the clean channel. I believe he favoured a DS-1 into a Marshall 6100.
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It could be either the channel switch or Dist stomp box.

I do both depending on what sound I am going for.

My amp is a Bugera 333xl which has a clean channel, a gain channel and a lead gain channel. I use one gain channel for normal Rock and hard blues, the other has the same settings but with a bit more gain for the AC/DC type stuff. On top of that I have 2 different distortion pedals with settings for 2 levels of the heavier stuff that I run thru my clean channel.

Playing live, you don't want to be mucking about changing your settings.
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i use a vox ac15 and i chose that amp because of it clean tones, i use the top boost channel for some blues and some punkrock, but when i need distortion and overdrive i kick in my blackstar ht -dual, which has a cruch and a lead channel (and even a clean channel :P)
so yeah, i use my tube amp mostly for the amazing clean sound
I remember once hearing that when satch was using the jsx's he wasn't using the amps distortion, just running his distortion/od pedals into the clean channel.
I've talked to plenty of guitarists who liked running a mess of overdrives and distortion stomp boxes just to have variety and options.
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Live use my crunch channel on the medium gain stage, of my 4 channel 100w Marshall tube half-stack, then drive it harder with a Digitech GNX4 using different stomp models for different covers. Big Muff for White Stripes stuff, Tube Screamer for Offspring, Fuzz factory for... you get the idea.

BTW, I way prefer the GNX4 over individual pedals for OD/fuzz/distortion, compression, noise gate, & whammy, but the delay and modulation effects suck.