Isn't it true that if you're on high edges at the end of a completed turn, that's where you'll have the most counter? And if you're on high edges at the fall line, then that's where you'll have the most counter? Counter correlates with highest edge angles, and that shifts from place to place in the turn depending on how your are making your turns.
I learned a new term this week: effective slope angle. That's the angle formed between your shins and the surface of the snow (the left-right angle, not fore-aft). As I understand it, the slope angle is zero when your shins are perpendicular to the slope. Experiencing a slope angle between your shins and the snow surface causes your uphill leg to move forward since the ski boots prohibit free flexing of the ankle, and bingo you have counter.
If I've got this right, then that slope angle is biggest when you are skiing with the highest edge angles, and so that's when counter tends to emerge the strongest. So you can ski into counter and have that counter happen at the fall line, or you can ski into counter and have that counter happen at the end of a completed turn. "Skiing into counter" does not mean the counter needs to happen at any particular place in the turn. It just describes the process of getting there.
Thinking in terms of this slope angle that helped me sort out the skiing-into-counter questions I've had.
I think of this countered position as "rhomboid". My inside (uphill) half moves forward with respect to my outside half, and I'm a rhombus. Not a square.