I'm a little fuzzy on how growth rates and stat caps work and how they interact. From what I can tell, each character has their own individual growth rates for each of their stats. This affects their chances of increasing a certain stat when they level up. For example, Unit X has a 30% growth rate for SPD. This means that whenever Unit X levels up, there's a 30% chance that the SPD stat will increase by 1. Different classes have no effect on the growth rate, so being a Barbarian or Myrmidon doesn't restrict my Avatar's MAG growth rate.
Stat caps, on the hand, vary between classes. Promoted classes (Dark Flier, Great Lord, Grandmaster, etc.) tend to have higher stat caps than their respective un-promoted classes. These stat caps describe how high you can go in a specific stat when you are in that specific class. Borrowing from my earlier example, Unit X has a stat cap of 20 for SPD in Class Y. As long as Unit X belongs to Class Y, his/her SPD cannot go above 20, no matter how much he/she levels.
Am I understanding this correctly?
P.S. What happens if you go from a promoted class to an un-promoted class after hitting the stat cap? I am of the understanding that your stats go down to the stat cap, but are these extra stats lost or are they regained if you raise the stat cap (by promotion or switching another class with a higher stat cap)?