Destiny is built to interact with the main game's existing worlds, not create separate, isolated universes of story or action. To this end, when playing something like The Dark Below, Destiny's first DLC pack due out in December, players will still run into characters going through the full campaign.
"The Dark Below is actually a really interesting expansion; it's got its own story," Bungie Director of Production Jonty Barnes told Joystiq at Gamescom. "We call it an expansion because it has one of all the activity types from Destiny, so it's story, strike and beyond – and competitive and cooperative experiences in there. As well as new gear, new armor, new weapons and everything else. Some of that attaches to existing places that you're familiar to, so you might find that as you're going through new areas, that you actually collide with players who are just playing the existing Destiny content. You'll have those collisions. We always want to create spaces where people can get together and cooperate, and we feel like that is a big innovation in Destiny."