No. Being a psychopath does not mean you are violent. That is a dangerous assumption.
If you'd study a high functioning psychopath in society instead of an inherently violent one, you'll get two very different people.
If you only conduct studies on violent psychopaths, what is your conclusion? Psychopaths are violent!
Of course it wouldn't be the same. Do you honestly think everyone diagnosed with psychopathy are pathological and violent, like criminal psychopaths?
Just like neurotypicals, some are violent, some are not. Some are anti-social, and some are not.
Nuances.
The biggest difference between a "normal" psychopath and a neurotypical, is that they don't reason with emotions. They are not guided by sentiment.
They do not love like neurotypicals do because they lack the chemicals. That doesn't mean they don't see value or appreciate people.
Or so I've been told.