You have defined fusion welding Nando. TIG's are by no means limited to fusion welding. You are correct though that it's not brazing. when I thought about it some I realized that brazing doesn't really melt the material being joined but rather introduces a material that binds the materials being joined.
Tig's usually use a rod (like in brazing) to introduce filler in the weld to intentionally manipulate the characteristics of the weld for strength or some other reason, to build up a surface or fill an area in. They are an extreamely handy toy.
The bellows I've refered to are pressed and rolled then ERW joined at the seam. Later sleaves are slide into the ends and fusion welded using a TIG to provide for a flange etc.
We must be refering to a different kind of bellows. I'm not sure where you got the idea that TIG welders strictly fusion weld especially if you have designed them!
Mike
P.S. I've used TIG welders and have never fusion welded with one and I'm sure a quick search of the net will define what MIG stands for.