Mind, is analogous to Spirit in other FF games, with what it does, so I assume it means basically the same thing.
Mental fortitude, or faith. General strength of mind to not be mentally overwhelmed.

Intelligence I attribute to raw processing power.
How quickly one can solve equations, and the complexity of puzzles one is able to solve.
This is different from wisdom or ingenuity, so you can roleplay it more easily.
Your character can do number crunching you wouldn't be able to, but won't necessarily be able to think of solutions to abstract problems that the player is supposed to navigate any better.