A major scale and its relative minor contain the same notes but do not have the same tonal center. C major and A minor both use C D E F G A B; the difference is where the music feels at rest.
Find the relative minor
The relative minor begins on the sixth degree of the major scale. In G major, the sixth note is E, so E minor is the relative. You can also move down three semitones from the major tonic.
Shared pitches, different function
In C major, C behaves like home. In A minor, Am takes that role. Looking at the pitch collection alone is not enough; listen to bass movement and cadences.
Why it matters when finding a key
A chart containing C, G, Am and F may point to C major or sometimes center around A minor depending on melody and resolution. Chord frequency alone cannot settle the question.
Practice
Write five major keys and their relative minors, then reverse the exercise. Play I–vi–IV–V and vi–IV–I–V and notice how the starting point changes your sense of center.