Those without a Square button to activate modify your natural X attacks. For instance, if ability A says: Extend your combo by pressing Square

Then it adds onto your attack when you press the Square button.

If ability B says: Attack an enemy while swinging left to right

Then it changes one of your normal, three hit combos to do a different attack.

Triangles can be used for both Auto-Abilities, and normal Reactions Commands. The best thing to do is to disable all Auto-Abilities (Auto-Valor, Auto-Limit, whatever), so that way, you ONLY get Reactions in a fight and don't waste that valuable MP. There's a second command screen if you press left or right on the D-Pad, which brings up a second command menu, which will allow for Manual Limit initiations, as well as Manually Summoning.

Personally, I ONLY used Valor during my game play, and I never touched Summons.