I apologize if I've missed your intention - I'm on a stupid amount of cold medication. Yay, flu season.
There are no separate "modes" in State of Decay. Part of the challenge of building SoD was keeping it streamlined to fit the intended format. So there's just the game. You play it.
The confusion comes from me, probably. This is an open world game. The tutorial section is pretty linear in that you are nudged from one area to the next while you're learning the game. But once you're done with that, it becomes entirely up to you.
If that freaks you out, you can just do the storyline missions. Those are fairly linear. They also may trigger irreversible world-changing events. Therefore, I've been cautioning people who just want to play the game as a sandbox to avoid those. Some of the world changing events have the potential to make it extremely difficult to build a sustainable community, for example.
So there's no sandbox "mode" or story "mode," it's just you making your preferred choices.