lets say you're playing C major at XX5588, which might be the main C major chord. 
can the same exact scale notes (allowed for that main C major chord) on the fretboard be played with the C major open chord X32010? 
or be played with a barred C major chord at 8 10 10 9 8 8? 
begginer geetarest.
The same notes yes it`s the same chord different positions it doesn`t matter even with octaves as long as the notes are correct it works.Scales are more of a separation of notes used for riffs bass lines etc.You mention C so it`s C,D,E,F,G,A,B,C all those notes aren`t used in a chord but it`s the scale.
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C major is C major, regardless of the position you use. Positions are irrelevant. There are many ways of playing the same chord, but it is the same chord. The same applies to scales. The C major scale is the C major scale and always has the same notes in it, regardless of the position you use.

C major = C D E F G A B

You can find the same notes in different positions and octaves.

Here are all the different ways you can play an E4 on a 6 string guitar. This is just to demonstrate that the same note can be played in many different positions.

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