I wrote this about the difference between exploration and wandering some time ago:
Exploration is not an aimless activity. It’s a very goal-driven activity. We might not know what our goal is initially, we might not know what we’re looking for, but we know we’re looking for something. It’s the knowledge (or assumption) of that “something” that drives us to look closely at the world, to explore it. Without that “something” to tempt us, our movement ceases to be exploration and becomes wandering. The former has a purpose (we move with the intention of learning), but the latter has no purpose. That’s why Skyrim gives us a compass to point us in the direction of interesting discoveries. Bethesda understood that without some sort of goal in mind, players can only wander, and wandering is boring.
I think the distinction still holds true. There’s a fine line between exploration and wandering, between something fun and something frustrating. The Elder Scrolls and Fallout games have achieved immense popularity because they expertly straddle that line. Surprisingly, so too does Pokemon Go.