Psychopaths are genetically wired to be unresponsive and they don't really feel any emotions so it's impossible for them to form interpersonal relationships. Psychopaths don't display fear, if they are in a near fatal car accident they appear cool and calm, they have no desire or need for companionship or friendship, they are basically just cold and dead inside.
A narcissist is the opposite, where the Psychopath needs no companionship and friendship and cares nothing for the opinions of others, a narcissist longs for the acceptance and admiration of others. Narcissists do feel, they feel shame, anger, sadness, jealously. Narcissists are all about other people, they want everybody to know that they are better or special, whereas the Psychopath doesn't give a single thought to the opinions of others and doesn't long for fame and admiration, they don't care.
Both share some common traits, such as a lack of empathy for the others, and reckless behaviour, but aside from that they are quite different inside.