Final Fantasy III is not a sequel to Final Fantasy II, they just share similar game mechanics and are set in comparable worlds. Each installment in the Final Fantasy series is like a new novel written by the same author; certain ideas or characters may be recycled, but the plots and settings used are independent of each other. By completely renewing the story line and the world for each new title, the series remains fresh and exciting even after 23 years.
Final Fantasy XIII is best known for revamping the gameplay battle-system in the series, as well as departing from the traditional single-protagonist story line progression. Instead of limiting the player's experience to that of a single character in the story, the game often steps back in time after an event to show the other character's side of the story. For example, in chapter 4: Separate Paths, the 6 main characters split apart into 3 teams of 2. The player follows the first 2 characters as they pursue an unknown figure in search of answers. After an enemy airship passes over the 2 party members, the game jumps back to when the 6 characters split, but this time upon departure, the player follows the path of the next 2 who decide to search for a way back home. After a brief time with these 2, they also witness the enemy airship pass, and the player is again brought back to the previous departure of the 6. The player then proceeds to follow the remaining 2 characters' story, until they eventually find themselves aboard the enemy airship, tying all 3 stories together. The story then continues to progress chronologically, following the different characters along their separate paths until they are eventually all reunited in chapter 11.
The unique interactive quality of video games allows the player to adopt the role of each character they play as. By controlling the behavior of the character, the player experiences a deep level of submersion into the story which other media types struggle to achieve.