What does having a higher rank do for me that a lower one doesn't?

For instance, I've gotten both 1% and 2% stat -> stat and both were C rank.

If I were to get stat -> stat but B rank, would this be higher? Or does this just not exist in B rank?

If I get an S rank line... what IAs does that mean I can get? All of them at ANY level of "goodness"? Or will being S rank guarantee that even if I get +dex for instance, that it'll only be a high amount of dex gain?

I hope I made that clear T.T