G sharp and A flat name the same equal-tempered pitch, following the pattern common to all five chromatic notes in this atlas. A flat is the spelling far more commonly seen in written music, since A flat major and its relative F minor use key signatures built more naturally within the standard system of fifths than G sharp's equivalent spellings would require, making A flat the practical default in most notated contexts even though the two names describe an identical pitch under modern equal temperament.
G sharp minor, by contrast, is the spelling more often retained in minor-key contexts, particularly as the raised leading tone within A minor and other closely related minor keys, illustrating how the choice between a pitch's two enharmonic names in practice depends heavily on the surrounding harmonic function rather than on any fixed rule assigning one name permanently to the pitch.
The choice between the two names also affects how the note is read at sight: a performer seeing G sharp in a score expects it to function as a raised step within a sharp leaning key or scale, while the same pitch written as A flat signals a flat leaning harmonic context, so the spelling itself carries information about the surrounding music beyond the bare pitch. Music theory calls this broader phenomenon enharmonic equivalence, the fact that equal temperament assigns the same sounding pitch to more than one written name, a byproduct of tuning the twelve tone scale to divide the octave into equal steps rather than preserving the slightly different pitches earlier tuning systems gave sharps and flats.