A G# Minor (G#m) chord contains the notes G#, D#, B. It is built from the minor formula 1 - ♭3 - 5, with G# as the root.
Why do the frets feel tighter on G# minor?
Fret spacing narrows as you move up the neck, so the same barre shape is physically more compressed at the 4th fret than at the 2nd. It's the same chord form as F#m — the hand just has less room.