Borderline Personality Disorder is not an actual mental illness although the distinction has been almost completely blurred.. It's an Axis II diagnosis which is used for, well, personality disorders, i.e., "flaws" in the development of personality as opposed to something malfunctioning in the brain's biochemistry. There are implications for treatment (because there is theoretically nothing wrong with brain function there was once an idea that it was inappropriate to prescribe psychoactive drugs though I imagine that's no longer the case) and insurance reimbursement (insurances used to refuse to pay for treatment of personality disorders as they weren't considered illnesses so we were always required to give personality disordered patients an Axis I diagnosis (a mental illness) whether we thought the patient had one or not in order to qualify for insurance reimbursement.
You might want to check the Diagnostic and Statistic Manual, it must be online now but a library would have it if not. There are quite a few personality disorders. The best definition I ever heard of personality disorders is that they're what happens when a person overuses one particular type of coping mechanism, e.g. attachment, anger, self involvement, etc. All of these are things we normally do but not excessively and in balance with other coping mechanisms. The overuse of one sort of behavior is what makes the condition pathological.
A real hallmark of someone diagnosed with BPD is a nearly desperate desire for closeness while simultaneously being threatened and frightened of having them. That creates a constant pattern of behaviors which draw people close and then doing things that push them away. They'll develop other problems, substance abuse is pretty common, so is suicidal gesturing. They're manipulative in tying to pull this off and generally makes them one of the least liked population among mental health professionals and honestly, I've seen lots of people assign that diagnosis to patients they don't like and find difficult. I generally refused to use it because it was generally prejudicial to the patient as they passed through other parts of the mental health system My guess is that your daughter did not make a good impression on whomever evaluated her. I never thought the mental health system did much for those people that was useful, maybe because most of them were in treatment because someone else thought they needed to be and they thought everyone else was the problem. And frequently they are at least partly correct.