People with BPD are typically surrounded by chaos of their own making. Rage, self-harm, suicidal behavior, intense emotional outbursts, alternating between idealizing people and devaluing them, extreme emotions, etc. are all symptoms of BPD.
Psychopaths (or sociopath, if you prefer; they're often used interchangably), may be impulsive and have poor behavioral controls, but they typically have blunted affect and are emotionally shallow.
In short, individuals with BPD have a surplus of emotion, while psychopaths have a deficit.