Pokemon hasn't been out that long here and came upon this forum looking up what triple battles were - turns out it's in the manual...like anyone reads those :/ - The turn table is rotation battles, it suggests you can move the table and make an attack in 1 turn so I assume you can attack with any of those 3 any turn but only hit whatever pokemon your opponent chooses...
While the triple battle allows all pokemon to fight each other, but the side pokemon can't attack the furthest pokemon from them on the chain. Which I like the sound of because otherwise you could just mob 1 pokemon with 3 hits every turn.
However, only had it a few days so it'll be interesting to find out if these modes are actually any good!