#1 Their Motivation
Different motivations influence the behavior of each type of individual in a unique way. In order to experience some form of hedonistic pleasure, the psychopath mistreats others. If they’re doing you any form of harm, they’re probably hurting you for wealth, sex, or indulgence.
However, narcissists abuse others in order to maintain their feeling of superiority. They are more focused on these because they want to have more control over their environment, fame, and admiration.
Consider the scenario when the psychopath and narcissist enter a bank. Unexpectedly, this bank is robbed at the exact same time. To continue boasting about how amazing they are, the narcissist may step in and attempt to be heroic. The psychopath, however, might take advantage of this to assault the robber and flee with the loot.