You’ve got that backwards. Sociopathy is the lack of ability to connect on a normal human level, hence the inexperience of love for another person. It’s solely social, not emotional. Psychopathy is the lack of ability to regulate emotions, or the spirit/soul, leading to uncontrolled outbursts, psyche=soul… -pathy is roughly as it sounds. The path a person uses, or means for functioning their current condition.
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I am positive you got it wrong because psychopaths can't experience emotional outbursts since they can't feel anything at all, they are completely emotionless and have to simulate their emotions to pretend to be normal, they are efficient manipulators, a famous fictional psychopath is Dr. Hannibal Lecter and you can also see the TV series Dexter about what psychopathy is for some examples among countless others.
As for sociopathy, it is the rejection of social norms, rules and laws, or to sum it up, the rejection of society.