From what I understand (and I'm by no means an expert), anxiety is often co-morbid with BPD. Personally, I consider my anxiety to primarily be a symptom because it's most often related to other BPD symptoms. For example, crippling anxiety that someone will leave or I'll be embarrassed/humiliated, stuff like that. But I guess if it's more generalised anxiety, it could be considered a seperate disorder?
Best wishes