There's a lot of confusion here, and we haven't done the best job ever of explaining the game or its structure.
I'm Luke, and I'm one of the lead designers on Destiny.
First, Destiny is structured into Activities.
We've attempted to build a suite of activities that can suit a variety of moods (I want something challenging! I want to chill out with my friends! I want to see where the story goes next! I want to shoot other players!, I want the game to be a cruel dominatrix! et cetera)
These activities come in a bunch of flavors:
Story missions - soloable activities (you can still play them in groups of up to 3!), often with ties to the main story arc of Destiny (the campaign). These activities appear at various Levels (numerical, relative to the player) and choosing a higher level (relative to you) means you're opting in for some additional challenge.
Strikes - 3 player activities, with bosses and loot at the end. Their goal is a highly replayable activity that will - at higher levels - lead you into the loot game.
Explore - cruise around the surface of a planet in Fireteams of up to 3, taking odd jobs and tasks for the City. You can find minerals and resources out in the world that you'll have some use for as you find weapons in Destiny that you want to stick with. This is a lower intensity activity
Raids - 6 player, cooperative required, communication required gameplay. High challenge. We haven't talked much about this yet and I'm not going start that conversation here on NeoGAF
Multiplayer This is for the "shoot other players" mood.
Now, the second part is how the world has been built.
We've structured Destiny's world to have places where you will probably intersect with other players, and places where you won't. We're not going to have players drop into the climax of a mission, but the common landing zones for a given planet? That seems like a great place to see other players running amok in the world.
EDIT: Regardless of what activity you're playing (PVP aside), you'll see players on their own activities, i.e., players beginning a Strike might see a guy collecting Relic Iron on Mars, and a Public Event begins and suddenly everyone is distracted to take down a key Cabal target for a chance at powerful gear and materials to upgrade your best weapons and armor.
A bunch of folks are playing the Alpha now and we're already seeing all kinds of opportunities for places to improve Destiny. I have no doubt that in the Public Beta, we will learn even more from your feedback and experiences.
I'm not going to get into any of the recurring activities or gearing or class stuff today, but I imagine we'll start to try and explain stuff more soon.
