I think bipolar is characterized by swings between exaggerated feelings of well-being with feelings of great depression. Borderline personality disorder, I think, is characterized by an almost permanent state of uncertainty -- being on the border of instability, prone to sudden swings of mood and thought. I think older theory was that this was a matter of personality, seen as so serious that it could not be changed -- something that therapists could not handle, and therefore they were more frustrated by or even frightened by.

So both conditions would share the traits of instability, but one has swings between extremes, swings that usually take place over hours or days, while borderline can produce much more rapid changes. Just as generalizations.

To someone familiar with "systems", you can see what might cause swings between extreme states -- this is characteristic of some systems, even physical, non-living ones, that get pushed out of equilibrium. Similar "pushes" away from equilibrium could cause a more general instability. But mental health types are usually not familiar with this kind of thinking.