Originally Posted by: JoeNovice"C6=(C,E,G,A)
Am/c=(A,C,E)
Nice try tough."

WRONG..... Am/C = (C,E,A,C,E) in open position. The symbol mean C in the bass.

C6= (C,E,A,C,E) in open position...... See?

If you can find all those notes on your guitar and can play them you will see they are identical. (minus the names of course)

C6 could either be a major 6th chord, C-E-G-A (which is essentially Am7 in first inversion) or, like I just said, a minor 7th chord, Am7, in first inversion. Or, hell, it could even be labeled C6 because IT's in first inversion, after all "6" is what you label first inversion chords with, right? That would make it E-G-C

I see where you're going with this, though. C E A C E. Yes, those are the same notes, but it's not the same chord. The chord behaves differently in each case, and that's why music theory does not just call them the same thing.