I use "balance" generically to refer to equilibration atop a fulcrum, and dynamic balance to refer to equilibration in motion. It is important in conversation to use proper semantics to avoid misunderstanding ... so the clarification on proper definitions is probably important. However, the mental image that passes through my mind when discussing BOS has nothing to do with balance. That to me is stability managed between two pillars.
The question asked previously about stability and balance being the same? Not for me. When the skis leave the surface of the snow, BOS no longer applies - at least for a period of time. Since I don't think in terms of BOS, there is no mental adjustment for the new orientation when my skis are off the ground. (Which is much less frequent than when I was younger.)
This all means nothing from a teaching standpoint, but just another experiential perspective thrown into the mix.