Described as a "Modal Chord", min9 is the tonic chord of the Aeolian Mode, and also of the Dorian Mode.
The difference is whether there is a Minor 6th note (Aeolian Mode), or a Major 6th note (Dorian Mode).
If you are improvising in the modal key signature of G# Aeolian, and playing this chord in combination with melody, then it makes sense to find mode shapes based around the 4th fret, for the G# Aeolian Mode.
Similarly so for the G# Dorian Mode. The Dorian Mode has a more strident sound or character, it could be said, and this is due to the musical interval between the Major 6th note and the Minor 3rd note. This is the distance of a "tri-tone", three tones, or six semitones. In other words, six frets' distance.
The Aeolian Mode has a softer sound, and will also interact nicely with the Harmonic Minor Scale as a way of slightly adjusting the sound.
There is a tri-tone interval somewhere in each of the seven modes, it just depends on where it is that does influence the sound and character of the mode. With the Aeolian Mode, the tri-tone interval exists between the Minor 6th note and the 9th (2nd) note. Somehow this provides a more lilting sound to the melody options.
As usual, these ideas on melody and the characteristic sound of modes are merely starting places for musical conversations, melody explorations, and harmonic structural progressions.