They're both concepts that try to encapsulate reality. Square pegs for Square holes. Rectangular pegs for Rectangular holes. There is some overlap but one won't necessarily fit the other.
If you tortured animals as a child, that's highly predictive for psychopathy.
If you steal from people, selectively torture someone, that's sociopathy. You see it all the time with offended snowflakes. These are the people who will throw nails by your car hoping you wind up with a flat. The people who will smile to your face then drop that fake smile the second you're not around.
Sociopaths and psychopaths know how to put on a mask, people with empathy have more consistent facial expressions because they're not wearing a mask, their expressions are natural and guided by emotions.
Sociopaths are only concerned with their own status and power. Yes a lot of our leaders show these traits.
Bill Gates is a classic sociopath, if you want a film study in sociopathy and narcissism watch him talk.
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