Grilling is done over direct heat, and yes, it can be done indoors with virtually any heat source, with the intent of quickly cooking the food.
BBQ is done with indirect heat... and in my opinion should only be done with wood or charcoal, with strong preference toward wood as the fuel source.
Smoking is done, with the sole intent of imparting smoke flavor on the food, not necessarily cooking the food, must involve wood to provide the smoke... but doesn't have to rely on wood as the soul source of heat, if more heat is needed.
It all could be done indoors, if you have enough ventilation... Temperature is incidental, but grilling is almost always done at temperatures of approximately 500F or more.
Most pellet grills do much better job at BBQ than grilling or smoking, but some rare ones, managed to do all three reasonably well.