The Volcano is actually a very simple piece of electronics in comparison to something like an Xbox or Playstation. It can be unplugged without consequence because it does not have any components inside of that need time to 'shut off' before the power is removed. I think the reason that the bag started filling again is because the switch for filling the bag must still have been 'on', so power was able to flow through it when you plugged it back in.
The switch does exactly the same thing as removing the cord, because it is wired directly to the wires that are coming into the unit from the cord. When it is switched off, no power can flow through it at all, which is a very safe and reliable design to make sure no short circuits or electronic faults can occur while it is off.
The gaming systems though (and computers in general really) are super complex systems, with various types of memory that gets used in the course of processing your data. You see, most data that we want to use in computing something is on a hard drive or a disk of some sort in these systems, and while these can hold a lot of data they run very slowly in comparison to the processor. So when you run a program, it gets loaded off of the disk and into your RAM so that everything runs as fast as possible. Pretty much everything that your using on these systems has been loaded into RAM, whether it is Windows or the part of GTA5 your playing.
Now RAM is memory, but it's not reliable memory. When you turn your computer off, everything in the RAM is erased. It's not a bug or a problem, it's just the way it works. RAM needs power to hold it's data, unlike disks or hard drives which can sit unpowered for years and still work. So anything that is being run within the RAM is instantly lost when you unplug the cord. This could be a file that is being edited, your game save, a core component of windows. Things that the computer never got the chance to take out of the RAM and put back on the hard drive before power was lost.
This is why if you pull the plug on a computer, it boots back up to normal windows instead of where you were before. And if you had a file you were working on and hadn't saved, you'll have lost it. To make matters worse, Windows and other OS's are constantly opening and editing system files behind the scenes, and they can sometime get corrupted in a loss of power and damage to the point where they stop working.
I'm simplifying things quite a bit here; but it certainly sounds to me like your really interested in electronics in general so if you want to learn more about it these are awesome places to learn about circuits and electronics design:
https://www.sparkfun.com/
http://www.adafruit.com/
http://www.youtube.com/user/Afrotechmods
http://www.youtube.com/user/makemagazine