Actually, they're totally different. quick magic is basically a one time chainspell, firing a spell off instantly and with 0 recast time, allowing it to be cast again right away. double cast wouldn't speed up casting at all, but is more like a "double damage" sort of buff, only it also works with status cures, healing magic, buffs, etc, and does not grant instant recast time like with quick magic. Sure sometimes it might not be useful for non-cure or damage spells, but doublecast erase? That might be nice.

And again, I realize it's probably deliciously overpowered and ridiculous, but it's that way because A) getting it would require you doing a gigantic part of the game and B) It's gotta appeal to all jobs. If the dev team thinks it's too much, they can always implement it with their own stats.