Basically, I know nothing about technical bits, but it seems entirely possible to me that you should be able to get a clear studio quality if the noise is directly inputted into a recording device, even when live? I figure there’s many different ways to record, so which one does this? Any info would be cool, ta.
This is more a query for a band I wanna get involved with, and it all hangs on getting decent live recordings really. There is a laptop, and loaads of wires… And the guy with the laptop is on the drums, which come in the form a squarepusher pad… everything is attached electrically… so I thought it’d be reasonable that in between the instrument and the amp there could be something that’d be able to record the individual sounds? So you could effectively have the basic clear quality notes as one recording, then the overall live recording? Or something? They edit it all over the place afterwards, but the problem is the quality ain’t great for making albums…. And it’s from live gigs that the best albums would be born. My technical language is pretty limp, so you might have answered this already but I wouldn’t know if you had… sorry to be so ignorant haha. Thanks for info so far 
Like Chris said, the sound guy will have an "out" (possibly several) but you are going to get his shitty mix in that out. The sound guy has no idea what you want to sound like.
My opinion…
Get a recording interface with enough ins to capture everything, and enough outs to send all the signals to the sound guy. This will likely be a rack mounted device compatible with your DAW. You will need your laptop with your DAW on stage. Not cheap.
The other option (good for using a mobile recording device or a DAW on your PC). Use DI boxes with multiple outs and a "thru" design (not the $30 ones). One out to the sound guy, one to your recording stuff (or amp, then from the amp to your recording stuff).
Prepare to spend some money and time and capturing acoustic drums properly.
*EDIT* If you are using highend multi effects boards or rackmounted effects boards for guitar or bass or vocals, you should have extra outs to send to a recording device.
*Edit again after your latest comments* I think I gotcha. Use DI boxes with the "thru" technology. Run from the digital instrument into the DI box. The DI box has two outs. One will go to the sound guy, and one will go to the laptop or amp (then to the laptop from the amp). Get an interface for the laptop that has enough inputs to capture all of the tracks. Use something like Ableton Live for the recordings (reliable on stage and uses minimal computer resources compared to other DAWs). With Ableton, you can record, run background sounds, and run DMX lights (with something like DMX IS) all at the same time.
The DI boxes you will be looking at are about $100 or a little more. They won’t color the sound too much, and will let you put the signal in multiple places. If you have a lot of inputs, this will do it too for much less money overall.
http://www.americanmusical.com/Item–i-ART-S83WAY
I have used several ART pre-amp devices and all but one has worked well (they sent me a new one for the one that pooped out). Can’t beat AMS on prices either, and they have a payment plan (which I have used a LOT!).
Also, if you can, get a backup for everything in case something poops out on stage.