Great to finally meet you in Snowbird, Gonz! I too am surprised at the confusion this thread has created about something that really isn't that complicated.
First, a few simple definitions:
1) Inclination: "deviation of the skier's body from its vertical axis." This is the definition from the Ottersen article linked to previously in this thread, and I agree with it (although I might suggest that "deviation of the body's long axis from vertical" actually expresses it more accurately). Inclination is simply the tipping of the body (center of mass) that I do to balance against the forces of a turn which, as PhysicsMan suggests, can (and must) occur whether I am flexed or extended, bent sideways or not.
2) Angulation: the creation of lateral angles in various joints, particularly the ankles, knees, hips, and spine. Angulation implies a more-or-less sideways bending in joints, although it may be more complicated than it first appears (knees don't bend sideways much, at least not more than once). Again as PhysicsMan describes, I can angulate regardless of my degree of inclination--I can angulate while standing still and vertical, or while tipped strongly into a turn.
3) Banking: tipping of the entire body into a turn--inclination without angulation. Banking should not be, but often is, confused with simple "inclination." Inclination and angulation are independent movements--one referring to movements of the center of mass, the other to relative positions of various body parts. Banking is simply the special case of inclination not accompanied by angulation--whether intentional or not. Sometimes it's functional; sometimes it's a mistake.
From these definitions, it is clear that inclination is a balancing move, and angulation is an edge-controlling move. We incline (lean in, "deviate from vertical") in turns on a bicycle, a unicycle, and while standing on a turning bus without holding on. We incline for balance in turns while walking, running, water-skiing, and inline skating. While it would not be inappropriate to refer to inclining specific body parts--i.e. "incline the lower leg"--the general, unqualified term "inclination" refers to the tipping of the center of mass into a turn.
It is important to note that, while inclination may play a big role in both creating edge angles and releasing them (when we return to vertical), it is not something we can use to CONTROL edge angles. At any given moment in a given turn, there is only one degree of inclination that results in balance. We can't incline more or less without losing balance, so inclination is not something we can adjust at will.
Angulation, on the other hand, has nothing to do with balance, so it IS something I can adjust for edge control. If I bank my entire body into a turn (inclination without angulation), and find that I don't have sufficient edge angle, I can't bank farther, but I CAN tip my lower body into the turn more while tipping my upper body toward the OUTSIDE of the turn. This is angulation, and clearly it serves no purpose other than to increase my edge angle.
Which brings me to my final point. There has been considerable debate, here and elsewhere, about whether it is preferable to incline or to angulate. First, by my definitions above, I believe that most people who pose this question really mean BANK or angulate. Angulation and banking are mutually exclusive; angulation and inclination are not. Second, the answer will depend on whether you need more or less edge angle at any given moment. It is not a choice to make in advance of a turn, not a question of "new vs. old technique," and not a question of individual preference, style, or free will. If you're in balance and you need more edge angle, angulate more--you can't incline more without losing your balance. If you don't, don't! If at any point you need LESS edge angle, reduce your angulation--because again, you can't reduce your inclination without losing your balance.
We can discuss the pros and cons of angulation in ankles, knees, hips, or spine, and we can discuss the various reasons why you might want more--or less--edge angle. But it makes no sense whatsoever to argue about the merits of banking vs. angulating as a general technique. One is not "better" than the other--they serve entirely different purposes. The two are not interchangeable. We don't have a choice!
For what it's worth, I will add that I think many skiers and instructors often do try to angulate too much. Beyond a certain point, more edge angle does not necessarily make skis hold better. More edge angle is not, in itself, always preferable to less edge angle, and surprisingly, it can actually make skis hold WORSE and carve LESS-cleanly. Especially with today's very deep-sidecut skis, more edge angle may make them want to carve a turn tighter than the turn I'm trying to make. In that case, reducing the edge angle to the minimum needed to hold will actually allow the skis to carve better, cleaner, and faster. This is why we see so much banking so much more often in racing today than before. It isn't a "new technique"--just a new opportunity sometimes afforded by our modern equipment.