The difference is that activated charcoal is burned at a higher temperature so it breaks down into a very fine powder which gives it a larger surface area than a chunk of charcoal on your grill.
So when a molecule passes through the tiny pores in the activated charcoal, those very weak charges make it cling to the carbon thanks to Van der Waals forces.
Activated charcoal is good at collecting molecules that contain carbon, like most poisons, because they’re usually large enough and have enough electrons to have stronger Van der Waals interactions.