Bipolar and Borderline Personality Disorder are quite different really and no, the treatments are not the same. With Bipolar, which is a mood disorder, they can treat with medications to help you find balance and the types of therapies used to aid people with dealing are also different. Cognitive Behavior Therapy is one that is used quite often.

With Borderline, which is a personality disorder, doesn't have meds specifically designed to treat it, while some meds are used to assist with states cause by the thinking process of those with Borderlins (like they may treat the depression aspect, or anxiety) The only treatment designed to help those with BPD recovery are some pretty intensive therapies (Like DBT, which has a very high success rate) and just general learning on how to manage and sway the through process.

Keep working with your doctors and do not worry about a label. They will figure out what the exact thing you need is and help you along the way. Treatment may vary depending on the diagnoses but you can still recover, and/or function with either diagnosis.