Big difference between smoking and grilling.
Smoking, to me, implies a long, slow (hours) cooking process at low temps, slowing bringing the temp of the sausage up to around 155 to 160 F. It then gets showered in cold water, dried, and is then stored until ready to cook and eat.The goal is to cook the sausage, while at the same time introducing smoke flavor and the preservation qualities of smoke, without excessive heat that will cause the fat in the meat to melt, leak out, etc. This is all temperature sensitive and due to the conditions, introduces the chance of botulism poisoning. You should not "smoke" sausage like this unless it has some nitrite cure in it. Nitrite causes the cooked product to turn pink and you can't tell what's going on without a thermometer.
Grilling....is get it cooked and let's eat. You can do a decent job of grilling a brat in under half an hour, even with indirect heat. The casing will be browned, some juice flowing and don't forget the mustard!