Not all Final Fantasy games are sequels, guys. There are improvements on graphics and gameplay, but nearly all of the stories are different.
Yeah, 13 variations on "A ragtag band of rebels battles a powerful Empire, only to discover that a greater evil is working behind the scenes."
Off topic: Your princess is in another castle?
On topic: Summaries=/=Storylines, obviously there are going to be some similarities, but a change in the characters, setting, background of the characters, and names of cities or items containing different meanings that are involved in the storyline make a very different story.
Let's compare two look alikes like Vaan and Zidane. *maybe spoilers*
Both of them are thieves and both of them are poor with no parents. But Zidane, unlike Vaan is a Genome whom is destined to be very powerful. Vaan just wants to be like a sky pirate.
There are crystals that contain importance in FFIX and FFXII, but for different purposes. The crystals(nethicite) in FFXII serve as powerful magic storyline wise, the Crystal(only one) in FFIX is what gave life to the universe and if destroyed, so is the universe.