I have been thrust into this ugly world since learning that my ex-son-in-law is a psychopath, so I will give you my take on this.
It can be difficult to distinguish between the two because they are much a like. They both only think of self, their wants and their needs and they both live to wreck havoc, lie, cheat and abuse those around them. They are both great manipulators-end result, to look good.
Narcissists only see themselves through others. They will create a situation (usually a negative feeling) and then watch your reaction. It pleases them when they see what they have created by looking at your face. They know that it was THEIR deeds that created your look, your fear, your sadness, etc. They need to be validated, they seek attention because it is their way of being, a NECESSARY function like "I need air to breathe," a Narcissist needs attention to live. When they no longer receive what they need, they rage and vent-not something anyone wants to live through. They have a conscience, so in order to do the evil they do, they will manipulate the situation so that they look good and you end up being the bad guy.
Psychopaths have no true feelings, believe themselves to be the smartest people on the planet (everyone else are pawns to be played with and used) Since psychopaths have no real identity, they learn from a young age to "fake" feelings, practice in front of mirrors expressions that come naturally to "normal" people. When the need comes, they can cry at a drop of a hat, pretend laughter and express almost any feeling-all from years of practice.
The are easily bored and invent games to stimulate excitement. Of course, people are the players in these games, pitting one against the other, pushing and prodding to see just how far they can go before they have reached their limit. They can express some feelings, like frustration, rage. Pity the person who fails to provide the psychopath the attention and admiration he is looking to receive.
Differences: The narcissist NEEDS to receive attention to feel good about themselves whereas a psychopath has no such need-they are perfect. A psychopath lives to be evil, always trying to one-up themselves whereas the narcissist is only evil when searching for and not getting the attention he needs.