Mine's an oldish 3-phase inverter TIG, has a 3-phase rectifier on the input without a neutral connection, and (relatively) tiny transformers between the phases to sense phase loss and shut it down. 3-phase rectifiers fed 3-phase have an easier life, and give the big pre-inverter DC bus capacitors an easier life with less ripple current.Oil cooled stick welders like Pickhill and Oxford, used 2 phases as that is all you need for a transformer. I would guess the more complex electronics of modern stuff will use all 3 phases, probably neutral as well.