Square-Enix seems to have used every type of battle system (with respect to time) in their many games. If you look up the Wikipedia entry, it looks like the only one they actually "own" is ATB. The thing is, ATB is a tad bit too generic nowadays (it was quite groundbreaking back then).
Quote:
On the battle screen, a status summary of each character is displayed. These encompass HP levels, MP levels (where applicable), and an ATB gauge.
The ATB gauge determines when a character can take action. When the gauge is filled completely, the player can issue an order to that character.
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Fully Turn Based battle takes us back to around Final Fantasy I when you issued all of your commands at once and watched your party and the enemy duke it out that round. That would be the most basic definition of "Turn Based". Some games still use this (ala Fire Emblem), so there's no copyright/trademark issue on this.
Then you have games that use a system sometimes called "Conditional Turn Based" (or CTB) which adds a crude time element into the system. Characters go based on their speed (how often they go) and as they go, time momentarily stops. I think this is the system used for Final Fantasy Tactics (and many other strategy games) and Final Fantasy X. This one I'm pretty sure nobody has a hold on since every turn-based strategy game (well, most of them) use it.
Then Active Time Battle (ATB) is basically the same as above, except time moves even when a player's turn occurs. This usually means you can be hit when selecting your action. This is my interpretation of it, and I don't think any other game has used this system, outside of Square games. I would have thought they dropped this system somewhere around the time of Final Fantasy IX, since everything above it used something else.
As far as Grandia goes, apparently, that's much like the ATB system conceptually, but it just wasn't called ATB.
So pretty much, Square just owns one branch of the Turn-based group. There could definitely be more turn based games coming out.
Jam it back in, in the dark.