So between 2 points where a great circle ain't formed,we have a small circle.
Now the smaller arc of this small circle would be the shortest distance between these 2 points.
NOOOOO... it's not the "smaller arc"... the shortest distance remains "part" of a Great Circle... the shortest distance between two globally defined points. If you were to continue "through" that defined point you'd eventually arrive back at the same position... a "Great Circle".