Those disorders are not closely related. Especially BPD and sociopathy, the symptoms are polar opposites. BPD is characterized by an inability to regulate abnormally strong emotions, not a lack of emotions.
Sorry I wasn't clearer: I was referring to colloquial use of the word, not what's actually clinically accurate. My experience has been that in everyday use "sociopath" can refer to any of the three, even if (as you mentioned) these are very different diagnoses.