I'm really confused with this. The CAGED system. It talks about scale patterns, 1,2,3,4,5. And then calls a given pattern or position the "E" shape for example, or G, or A, whatever. Does that actually have something to do with a physical shape? I'm getting bogged down with this.
From a chord shape perspective, it represents the 5 basic 'open' shapes that major chords can be played with on guitar.Each one can then be played with a similar shape, with a barre behind it, Couple of examples - use the E shape, but barre on the 7th fret, we make C. Use the A shape but barre on the 3rd fret, we make C again. Use the open C shape, but barre on the 5th fret, we get F. The one I feel is a little nebulous is the D shape, which only gives 4 (or 5) strings, and to me isn't that good to play. Put all the letters together to make CAGED.
Now, when it comes to the scale side of CAGED, it's a bit more hazy. Using the chord shape as a starting point, that will give us the 1, 3 and 5 of the major scale, and once we can establish the 1, we fill the gaps, using the actual string/fret places found in the chord. 6th string for E and G, 5th for A and C, and 4th for D.
Some players find this mapping helpful - I don't particularly. Rather like some will use a 4 fret span, and play scale notes below and above the root - as for example, the E shape on 5th fret, giving the root on bottom string on that 5th fret, but the 4th fret is also available with a finger ready for it. Play from there, and you have G# Locrian. Clever stuff! - but not that useful - to me at least!
The open/barre chord shapes that you are probably familiar with are contained within the pattern.
For example if you take an open C chord starting on the 3rd fret of the 5th string you have the C, E, and G notes of the C major scale. If you then fill in the other notes of C major around this chord fingering you'll have the CAGED "C" shape in open position.
But I wouldn't worry too much about the reasoning behind the names. I've never found that aspect of CAGED that helpful. Just learn the shapes and call them what you want.