Stability is how much the crosshairs jump when you fire a shot. Higher stability means less of a bounce. Different guns have different recoil directions; stability just reduces how 'hard' the gun jumps in that recoil direction, it doesn't change the direction or the area of the arc it can recoil in (to my knowledge). So an auto rifle that bounces in the 180 arc around the top will still bounce around that same arc, just bounce less. Handling is how fast you pull out the weapon when switching to it, how fast you go to aim down the sites, and how quickly you can control where the crosshairs aim when aiming down sights (the last one is mostly moot because one can simply up the sensitivity to move faster overall).