Hi, jaad. Plain old chords are 3 notes, but there are 6 strings on a guitar, so what happens is that some of those required notes are repeated in other octaves. Of course, you don't have to play anything but three-not chords, but why waste those extra strings?
That C chord you mention: X32010 ... XCEGCE
Notes in a chord can come in any order -- it sounds strongest with the root as bass note -- but any combination of C-E-G will be a C chord, even if it's the bass player playing the C, a trumpet playing the E and a singer humming the G ... the overall sound will still be a C chord.
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