Shipwright,
Before some "techno" corrects me, I will modify one of my previous statements. Techinically speaking, there are two welding processes being talked about here: the solid wire one is called Gas Metal Arc Welding or GMAW, the other is called Flux-Core Arc Welding or FCAW. Both identical except one uses a shielding gas that is provided from a flux within the tubular wire.

Unless your VERY anal, these would be generally referred to as MIG.

Stuart.