Each Final Fantasy game is different. There is a different world, a different story, and different characters per game. (There is, however, a certain Dissidia Final Fantasy, which is like Super Smash Brothers with FF characters.)
There are currently thirteen mainstream games with a fourteenth in the making (not counting the spinoffs). The most popular is Final Fantasy VII, which is the one you played. It had two sequels and a prequel made after it was released, and a movie. Is Final Fantasy VII: Advent Children the 'movie' you watched, or is it the anime Final Fantasy Unlimited, which is has nothing to do with the games at all?
Also see finalfantasy.wikia.com.
The movie has nothing to do with the games. It is just coincidentially called Final Fantasy. The games are all different and have nothing to do with each other. There is no theme.