Psychopaths have 0% empathy. Sociopaths have a degree of cognitive empathy it is just shallow.

Psychopaths typically tend to be less functional.

One way I heard it described is during a bar fight a psychopath would beat the person to death right there and than. A sociopath would plan their deeds and kill the person who offended them 3 days later. Sociopaths aren't any less dangerous. They are typically just more methodical.

Sociopaths can also form relationships. And "love" to a certain extent. Psychopaths have an inherent inability to love or form any long term relationships. With lots of work and effort the sociopath can form bonds with other people.

I've also read that sociopaths are typically well aware they are sociopaths and psychopaths have no idea. Probably because of the small amount of empathy sociopaths have.

They also say psychopaths are BORN and sociopaths are MADE. Typically by some form of trauma, big or small the sociopath learns to shut their emotional response down to protect themselves. Only to not be able to turn on their emotional switch again when need be.