"Wedge" refers to any time the skis ride on "opposing edges" (both inside edges) with their tips closer together than their tails.
A "Wedge Turn" is a turn made with the skis in a wedge, from start to finish. While it seems simple enough, there are as many fundamentally different ways to make a wedge turn as there are to make a parallel turn!
A "Christy" is a turn made with the skis on "corresponding edges" (both right or both left edges)--like a parallel turn, although the skis can converge (tips closer than tails) and tip to corresponding edges also.
A "Wedge Christy," then (I know, you didn't ask about this one) is a turn that begins in a wedge and ends in a christie, usually parallel.
A "Stem" is like a "half-wedge"--it occurs whenever the skier brushes one or the other ski out to a converging arrangement.
A "Stem Christy" is a turn that begins, then, with a brush out of one ski tail, with a "matching" move later in the turn to bring the skis parallel, or at least onto corresponding edges. There are "upstem christies" that begin by brushing the uphill ski tail out, and "downstem christies," that begin by brushing the downhill tail out.
"Step" refers to lifting and displacing a ski, usually before transferring weight to it to initiate a turn. "Step Christies" are simply turns initiated with a step. Steps can be "converging"--tails apart, "diverging"--tips apart, or "parallel"--keeping the skis parallel and just stepping a ski sideways.
All these moves have their places in contemporary skiing, although we tend to see them, and need them, much less than we used to, before the advent of today's deep-sidecut skis.
These are very basic, general descriptions--I hope they help. These concepts have indeed been discussed in great detail elsewhere in the forum--search the archives if you would like more information.
Or just ask....