I would think that wrapping in a pan covered with foil is braizing .
Wrapping the meat TIGHTLY in foil is important because you don't get braizing. This is the idea behind wrapping a brisket in butcher paper, the meat does not braize or steam, it still breathes. Its also the idea behind wrapping after the meat has come out of the stall, the juices have evaporated during the stall. The purpose for wrapping is the meat has taken on enough smoke, it has good color and bark, and ya want to preserve that while bringing the IT up to doneness.
Braizing could make your meat very tender, but also make it mushy. The meat is cooking in its own juices. It creates a different texture. Braizing would also destroy your bark.