Character skillsets. Each character gets a different set of skills from those available to the main characters. Umaro will get two.
Natural abilities. The starting Rages, Lores, and natural Magic of whoever has those skills has been shuffled around.
Treasure chests. All treasure chests in the game, save for the Striker in the Cave of the Veldt, are randomized. The treasure you get will be fairly close in value to the original contents.
Specifically, who can equip what. This also accounts for starting equipment.
The names of the characters are changed, pulling from all the names in Final Fantasy.
Expect some funny looking characters.
The spells they teach, and the rate they teach at have been shuffled around. It will be generally easier to learn spells now. However, there is no guarantee every spell will be available.
Items that appear in shops are shuffled around, except the Sprint Shoes.
Enemy steals and drops. Enemies themselves haven’t changed, but what they drop has.
Colosseum won items. Good luck finding the items you want from the Colosseum!
RNG Table. Final Fantasy 6 has a lot of things that can be manipulated by a knowledgeable player: Auctions, Doom Gaze, Slots, Encounters. With the RNG table generated at random, these events are now much harder to manipulate.