I'm not sure what you are looking at but what's important to remember is that every C, every D, every E, F, G, A and B anywhere on the guitar (or piano or whatever) are part of the C major scale. The C note found on the 8th fret of the 6th string (the low E string) is C3 (C note in the 3rd octave). If you start on that note and go up from C to D to E, F, G, A and B, you will play the C major scale using just the notes in the 3rd octave. If you play the A and B notes on the 5th and 7th frets of the low E string you will still be playing notes from the C major scale but the A and B are from the 2nd octave. It's common, when practicing, to play through the notes of a scale starting on the root note but no matter where you start you're still playing notes from the C scale (assuming you're sticking to C, D, E, F, G, A, B and C).

A little more advanced: If you are actually making music and are treating a note other than C as your home base (e.g., your melodies start and end there), it might be more accurate to say you are playing a mode of the major scale. The modes have Greek-sounding names.

CDEFGAB - the standard major scale mode (also called Ionian)

DEFGABC - dorian mode

EFGABCD - phrygian mode

FGABCDE - lydian mode

GABCDE - mixolydian mode

ABCDEFG - minor or aeolian mode

BCDEFGA - locrian mode

The intervals between consecutive notes are not all the same (some are a half step [1 fret] and others a whole step [2 frets]). For example, the interval between B and C is a half step whereas the interval between C and D is a whole step. These intervals are distributed variably across the major scale (in basic C major or C Ionian, the sequence is whole step, whole step, half step, whole step, whole step, whole step, half step). When you start and end on different notes, the sequence of intervals and the resulting feel is different. If you start and end on A, you are probably playing in A minor (aeolian) even the notes are the same as if you were playing in C major. But it feels different.