Yeah, what you're talking about, playing a C major scale starting on G, is a mixolydian scale. So it goes like this, in the key of C:
C D E F G A B C - Ionian (natural major)
D E F G A B C D - Dorian (starting on D, the second scale degreee.
E F G A B C D E - Phrygian
F G A B C D E F -...