The first type is what he calls Story of the World. This is the over-arching narrative that deals with the biggest threat to the world (the Elder Dragons) and how it is to be countered. ArenaNet chose to use dynamic events to tell these stories so that players are gradually made aware of the threat.
The second story type is your personal one, which tells of your own rise to power, fame, and glory in a variety of ways. Finally, there's the story of the five central iconic characters in the game (Destiny's Edge) and how they relate to you and each other.