It's also completely possible to use purchased adventure modules in sandbox play. In fact, purchased modules make things a lot easier, since you don't always know which way the players are going to jump. To use some classic examples, if the players decide to hire up as mercenaries to defend the free lands against the scourge of the Slave Lords, then you can run them through the four-part Slave Lord adventures. If, instead, they decide they want to tackle (literally) bigger challenges, they can head north to fight Against the Giants. Either could lead to Descent into the Depths of the Earth, or, if the players don't want to follow up on those clues, to something else entirely. The key is to give the players the choice in what challenges they tackle.

The key to a sandbox is to give the players the choice in what challenges they tackle. "Adventure module" isn't the opposite of "sandbox", either. It's completely possible to use purchased adventure modules in sandbox play.

In fact, purchased modules make things a lot easier, since they provide a lot of focused material to populate a sandbox quickly and you don't always know which way the players are going to jump. To use some classic examples, if the players decide to hire up as mercenaries to defend the free lands against the scourge of the Slave Lords, then you can run them through the four-part Slave Lord adventures. If, instead, they decide they want to tackle (literally) bigger challenges, they can head north to fight Against the Giants. Either could lead to Descent into the Depths of the Earth, or, if the players don't want to follow up on those clues, to something else entirely.

That freedom to go where they want and choose the challenges they tackle is what makes a game into a sandbox.