So whats the real difference between roots and stuns?

So, Snare and stuns. Both restrict movement, but one is able to prevent counteraction. Another difference is that snares tend to last longer than stuns.

So which one is rather a better option? I'd, myself, would say stuns, since you can't do anything during that time of incapability. So, I wanna make a suggestion for those snares. We all know disruptions, knock ups and the such, will stop any movement, but thematically it would make sense of a snare to do so too. A snare is something putting you to the ground, preventing movement, like Swain's snare and Morg's.

So to give snares the extra competition to deal with those mobile champs, could we make it where a snare will instantly lock them down, negating any movement, whether or not they are already in movement? It just instantly grounds them, removing all movement.

Edit: Examples include Vi not finishing her Q flight; Jarvan not finishing his flag dash, Nautilis not finishing his anchor throw.