There are a lot of shared symptoms between those two disorders, so it can be hard to tell, especially depending on how much time the docs were able to spend with you. I'd suggest reading up on both and seeing what you can identify with - there are "for Dummies" books for both disorders. You could be both, but it's not all that likely.

Some of the differentiating factors are black/white thinking, poor relationships, extreme fear of abandonment, and event-based mood swings for BPD. There's often a history of abuse or trauma with BPD as well. These things may also occur for bipolar, but as far as I can tell, there may be more of a predictable pattern to bipolar behavior and mood swings. I'm sure there's more nuance to it (I'm not a doc!) but that's what I've been able to figure out from reading and the questions my pdoc asked me. Part of the difference is that BPD is a personality disorder (environmental causes for "maladaptive" thinking, though not your fault) and bipolar is a mood disorder (biologically based). It's somewhat easier to correct thought patterns with therapy, but neurochemistry usually has to be addressed with meds, and in any case, usually the person will need both.

As my pdoc said, the label doesn't necessarily matter as much as good treatment does. Both are likely to be treated with meds + therapy, but meds are less decisively helpful for BPD, while therapy (especially dialectical) has been shown to work very well. And as people here will tell you, meds are very helpful for bipolar, and so is therapy, but therapy alone is rarely enough. The same meds are used to treat both, depending on symptoms.

Another difference is the prognosis (this was according to the pdoc). With therapy, most people with BPD get better enough to be close to normal and have relatively few symptoms. Unfortunately, bipolar tends to get worse over time, especially without treatment, and there tend to be more health complications due to the toll that behaviors associated with mania and depression take on the body.

But like you, I want to know what category I fall into, mostly so I know what I should be expecting for the long term. I'll probably have to go through a fourth and fifth evaluation for this before I can get a solid dx. So for you, whether to see a third pdoc would depend on what your concerns are with respect to the dx.