RetroGaming

Correct. Each game is it's own story. The characters, worlds, lore, enemies, even types of magic and how it works are all different in each game. The combat system is also different in every game, although always staying with in turn based until the later titles. It's an anthology series, each one is self contained.

Some themes are present in more than one. The use of crystals was a big story element in a bunch of them. Names are reused for newer characters and other things, which can make it fun when you recognize a name and see how much the character holding it is different. The character Cid is a great example, he might be a main party member or an NPC in a town. When you got a weapon that was badass in previous titles you knew it would be a keeper.

Spell names are probably the most consistent thing in the series. Summon spells especially were something people looked forward to in each new game. What was summoning Ifrit going to be like in this game?

Going through the games in order is fun because you can see how the games changed and built on each one as they came out.