'Cares nothing for others' is but one criterion and it's common to both aberrant personalities. A psychopath doesn't care about others, but doesn't require the adoration and attention of others. A stealthy serial killer is a psychopath but not a narcissist.
Many narcissists steal, but not all thieves are narcissists.
While all narcissists may be psychopaths, not all psychopaths are narcissists. The notion of a 'benign' or 'situationally acquired' narcissism is controversial in the mental health community. Consider a rock star or actor whose fame has gone to his head. Is being obnoxious psychopathic?
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