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Root Note of a Chord: Movement Up or Down
In harmony, the distinction is that C – G is considered a harmonic movement “up” because you get to the root note of the next chord by going “forward” alphabetically from the root note of the first chord to the root note of the next one in the progression. Like this: C – D – E – F – G.
The progression G – C is considered a harmonic movement “down” because you get to the root note of the next chord by going “backward” alphabetically, from the root note of the first chord to the root note of the next one in the progression. Like this: G – F – E – D – C.
Unlike in melody, the harmonic terms “up” and “down” with respect to interval movements (chord changes) have nothing whatsoever to do with pitch change. Unlike in melody, the chord change G – C does not mean that the chord C is “higher” or “lower” in pitch than the chord G.