Well, all FF's are the same genre, RPG. But whether or not they have swords and magic doesn't make them a different genre.
FF 1-5 were pretty much the swords and sorcery variety, with some machines such as air ships... then in FF6 you start to see more technology with magitek armor, lasers, guns... then FF7&8 were in a very futuristic setting complete with space travel. Then Sqaure decided to make 9 more retro, sort of a tribute to the very early Final Fantasy's, but the last solo FF to be set in a swords and sorcery world with what everyone calls super-deformed characters, or little people as they prefer to be called.
So with FF10 + will all be more of a sci-fi feel instead of a pure fantasy I'm guessing, but who knows what Squenix will decide to do now.