Cooking at low temps results in a finish that is more even end-to-end, sides-to-center, i.e., for example, medium-rare throughout. One can cook to, say, 125˚, as you note (or bit higher if desired), and then sear to finish. I prefer a more direct route, by, say, dropping the meat grate directly to the coal ring, but one can certainly sear in the oven or on the stove. Resting is not required first. One can smoke or roast to a desired internal temp then sear immediately. Rest after searing, before slicing for service.
Cooking start-to-finish at higher temps results in a finish that is less done at the center, more done at the sides and, especially, the ends. This is useful when one wants a range of doneness - more medium or medium-well for Uncle Harry, sliced from the ends, more toward medium-rare in the center for you.