Sorry, I use those abbreviations so routinely I've forgotten they're not part of common usage for all skiers. So thanks for asking. CA = counteracting, which means turning the torso (from the hips up) in the opposite direction the skis are turning (as opposed to being square to the skis). CB = counterbalancing, which means tipping the torso (from the hips up) in the opposite direction the skis are tipping (so even in a high-angled turned, your torso -- hips included -- will be level, or nearly so). So I suppose you could call CA "counter-turning", and CB "counter-tipping". You can see both of these especially clearly in the 2nd pic in this post http://www.epicski.com/t/143149/the-best-technical-advice/120#post_1933154
But those are added details to the tip which, upon further thought, I think I can now better summarize: The ability to balance comfortably on one ski isn't just one of several skills it's good to have; rather, it's the thing that needs to be in place in order for all the other skills to work.
For bonus points, what exactly do you mean by "you want to be able to initiate and regulate the turns by continuous tipping of the inside foot"? If you're balanced on the outside ski and can lift the inside at any point, what exactly is the inside ski controlling? (This may be clearer while actually skiing, but it sounds contradictory in writing.)
That's an excellent question, but unfortunately opens up a whole can of worms, and deserves a separate thread (indeed, there have been a few on this, e.g.,http://www.epicski.com/t/141727/inside-tipping-and-outside-engagement). But, briefly, the idea is that tipping the inside foot activates the base of a kinetic chain that in turn causes your inside knee, and then your femur, then your hip to move into the turn, which then gets the outside ski up on edge as a reaction, without your having to directly tip the outside ski (you just allow it to follow the inside) Why is this important? Well, you really want parallel shins, and the outside ski naturally tips in more easily than the inside (leading to an A-frame), so if you focus specifically on the inside, the outside will just take care of itself. The other idea is that you want "angles before pressure," so this approach allows you to set up your angles, in a balanced way, so you can then be ready to receive the pressure as the turn develops. I.e., you don't want to actively push on a non-angled outside ski at the top of the turn, because that can cause a pivot-skid. The summary is the inside ski provides the active guidance, the outside the stable platform.
[Some of you will recognize the ideas in this post as coming from he-who-shall-not-be-named. I find this state of affairs unfortunate since, if you're going to share someone's ideas, under normal circumstances you'd want to give them explicit credit, and he certainly deserves credit for these; IMO they're innovative. OTOH, he also certainly bears a significant portion of the responsibility for the current situation. In any event: Unpiste, if you want more info, PM me.]
Edited by chemist - 11/5/15 at 10:26pm