IMO

An addiction comes from wanting pleasure from, whereas a compulsion is something that is done to make things feel safe.

If you have a compulsion to check the door, swich the light off or wash your hands non stop there is no pleasure in doing so. That comes from trying to make the anxiety feel safe.

An addiction to a substance comes from the pleasure that comes from the substance in the first place and then it's doubly difficult to stop.

Sexual addiction that would come from the pleasure aspect, just as in smoking or alcohol.

Over-eating would be an addiction if it was just over-eating but it becomes a disorder when it gets out of control and becomes anorexia or bulimia.

Not sure what you mean in saying that compulsion/obsession is due to a narcissistic personality???

Anyway, I hope this helps.