I think a lot of the differing semantics may result from our different backgrounds.
I come from a racing background, where it's pretty clearly defined; if you have ever competed in, or coached at, a World Cup downhill or super G, you soon learn the difference between a ski that is carving cleanly and a ski that is skidding - even minutely. In the end, the clock is the best judge; if you win a section, you have probably carved that section more cleanly than anyone else. (Yes, I know, there are other factors, especially on the flats.)
However, I totally concede that ski instructors, freeskiers, mogul skiers, etc, may all have differing definitions of the term "carving" from World Cup racers - hey, that's what makes these debates interesting!
Of course, pivoting, stivoting, drifting, etc are also all legitimate tactics in racing - they are things racers do when they are not carving.
Good posting .
How about this...
Carving vs Skidding:
Edge locked = Carving
Edge not locked = Skidding
Carving = minimum friction, maximum speed and edge hold
Brushing (skidding) = scrubbing edges mildly against the snow to slow down or to tweek turn radius
Pivot (skidding) = turning skis sideways to slow down
Stivot (skidding) = turn starting off with a pivot to slow down or to correct the line and then hook your edges into a carve
etc. (add more tactics here)
These are just suggested definitions and tactis. Feel free to correct and add more.