Dennis - The last I heard (in Networking/Communications class circa 2002) the current theory is that a SIGNAL (as opposed to power) travels on the outside of the wire: especially important for coaxial cabling layouts.
With so many of these applications (like Variable Frequency AC Drives), when you get deeply into the internals, DC current is used to control AC Frequency or visa-versa. I'm not certain how welders work, but at one time I was told that large capacitors were involved. Capacitors block current, but pass voltage; transformers, on the other hand, can induce current (by virtue of the field effect) but the polarity of the ensuing voltage reverses (if I remember correctly).
The point I was trying to make in my previous post is that in practical application "power" is more than Current times Voltage (P=IE, or P=IV depending on your vintage). Power TRANSMISSION is a science unto itself.
(Did you hear about the Russians who tried to run LOW-voltage power transmission lines --the cables required a gauge that limited the distance the power could travel as well as increased the cost of the project prohibitively-- higher voltage is better for power transmission.)
As far as welding is concerned, I believe there are both AC and DC welding machines / techniques. Anything AC is sensitive to frequency, anything DC is sensitive to attenuation. The semi-conductors are in there to balance out all the relevant factors so guys like you and I don't have to think about them and overload our brain cells.
Under Edit: Art makes a good point --bigger is better!