Alright, I've been wondering about this for frickin' years and never found a direct answer. Here goes.

What's the difference between the Choco/Mog Materia's "Deathblow!!" and "Fat-Chocobo"? I assume the latter doesn't inflict Stop on the enemy like Deathblow!! does, rather it deals more damage.

And what actually influences whether you'll get Fat-Chocobo or not?