Not trying to be argumentative, but aren't you talking about welding either tig or gas in your second example. Seems unecesarilly confusing to refer to that as brazing. If you fuse the metals it's welding if you melt them together it's brazing. If you use the same metal as the parent in the rod, roughly, it is welding, use soemthing significantly different with a much lower melt temperature for an essentially mechanical bond, and it's brazing. The fact one uses a rod in both is irrelevant.