Mostly.
Every Final Fantasy has a new setting, story, world and characters. The only thing that connects them to each other is:
- Certain animals: Chocobos, Moogles.
- Fiends: Bomb, Tonberry, Cactuar
- Monster summons: The summons Shiva, Ifrit and Bahamut. The summons has changed names though, from eidolons, to aeons to espers and so on.
There's always a character named Cid.
- More that i don't remember.
As previously stated, the only FF that had a direct sequel was FFX-2 (FF10-2). FFXII (FF12) is a whole new one.