Introduction Plenty of guitarists learn chords arbitrarily, in that I mean they learn the shapes easiest to the instrument. There's nothing wrong with that in certain scenarios when it's stylistically correct, however when playing solo guitar or accompanying a vocalist there is sometimes call for other voicings and shapes.
Most people learn E, D, C, G and A at some point or another. And most guitarists will have learn E and A bar-chords, meaning that that part is really covered, so what remains to be seen is how C, G and D shape bar-chords can work. Some people who might have dabbled in blues or jazz will have played '9th' (i.e in C, x 3 2 3 3 x) - this is in-fact built on a C shape, which it's still not a million miles away from (x 3 2 0 1 x).
The CAGED system is a framework to teach all chords across the fretboard, most obviously this means there's a wider variety in where you can play the chord, but it can be easier to change from other chords in this position and you have an entirely new top note, which may complement or juxtapose the melody nicely.
So, simply looking at C, here are its 5 inversions, some much easier to finger than others, with the 'shape' listed next to it.
Minors can be derived from this by moving the '3rd', which in the case of C is E - moving this to Eb will give you the minor chord.
Shell chords are normally chords that done use the 5th, or just use the 'important' notes that give the 'gender' of chord away. In jazz you would assume the bass player or you left hand on piano would spell out enough of the chord, meaning you can reduce what you play.
Some examples of shapes, this one, again, built around the C shape
If you want to push the boat out...
In the above example you can see how each time just one notes changes, same shape still in C, another shell, built around 'E' shape