With the touch of a button, you can run and fight at twice the speed. That's a player-friendly quality of life update right there. There's also a New Game + and New Game -, the latter of which allows you to play without the characters gaining experience. Hard core modes for hard core players.
The name "Zodiac Job System" isn't just another case of a Japanese game having a word salad title. It's a direct reference to the biggest change from vanilla Final Fantasy XII.
(Screenshot from a PC emulation using an English patch. FFXII International: Zodiac Job System is officially only in Japanese. The re-release added English voices, but not text.)
These job class choices are permanent -- you pick when you get the character, there can only be a max of one character per job class, and there is no going back. Each job has its own custom license board with unique abilities and progression possibilities. This leads to...
In regular FFXII, you could see what was right next to an opened space on the license board, but in ZJS, you can see what every space on the board will become, meaning you can plan further in advance where you'd like to take your character development.
New to this version, you can control guest characters -- even make them your leader if you want to. You can edit their gambits, so they're not acting in their own pre-programmed ways, but doing what you would do. Oh, speaking of Gambits...
All Gambits become available for purchase at once, fairly early in the story, whereas they came much more gradually in vanilla XII. As well, there are 16 new gambits to make your team more customized than before.
You can take control of summoned monsters now.
The original PS2 box art.
This game was only released in Japan. Other Square Enix remasters have used the updated versions every time there's been one to draw from, so I predict this time will be no different.
With added Gambits and the job system, your playthrough is much more your own than in the regular edition of the game. Want Fran to shoot guns? Sure. Think Vaan is more suited to a White Mage than a Knight? Go for it.
I asked a game shop to give me a poster with this picture, but FFXII Int: ZJS was still new at the time, so they wouldn't give it up. This is just here because I like the image.