Namco Bandai’s Sword Art Online for the PSP has a story different from the anime.
In the PSP version, a mysterious system error occurs in Aincrad, the 100-floor world of the in-game MMO ‘Sword Art Online’. The game becomes realized on the 75th floor of Aincrad and beyond. Players are tasked with climbing the next 25 stories. Just like the anime, there are bosses on each floor, but there are also mobs over level 90.
You’ll play as Kirito, the main character of the anime, who can be equipped with a number of weapons, including: a one-handed sword, dual swords, dual axes, a dagger, or a rapier. Each weapon will have its own Sword Skills. In addition to skills which appeared in the anime, there will also be skills outside battle. New, unique skills will appear by continuing the “Sword Arts School.”