Story is one of the main modes in the Tekken games. It usually consists of 7-9 battles (depending on the game) and has at least 2 story driven levels (Tekken 4 and Tekken 5). It also contains one sub-boss (unique to each character, aside from Tekken 5, where Devil Jin is the sub-boss for most characters) and the final boss (each game has its own final boss). Each time Story mode is completed with a different character, it unlocks a new character to be used.
In the PlayStation 3 and Xbox 360 versions of Tekken 6, Scenario Campaign and its sub-mode, Arena mode, is that game's Story mode. However, in the PlayStation Portable version, it has the usual story mode. Tekken 6 Arena Mode consists of 4 stages akin to PSP's Story Mode.
It is not to be confused with Arcade mode in Tekken 5 and Tekken 6.