A Kappa and a Nupe both refer to members of the Kappa Alpha Psi fraternity. Both terms mean the same, but how they are used and when they are used is the biggest difference to be found.
The term Kappa is just a shortened version of the Kappa Alpha Psi fraternity. Each member that goes through the entire process of joining the fraternity can be referred to as a Kappa. The term Nupe is a less common name for someone in the fraternity, but it is not commonly used on most college campuses. Most members do not actually know how or where the term Nupe was invented to refer to a member of the fraternity. A few decades ago, the term Nupe was used to refer to a person once they were successful in becoming a full member. On the other hand, anyone that is in the process of pledging to the fraternity can refer to themselves as Kappas. However, some of the Kappa Alpha Psi fraternities throughout the states do use the term Nupe when creating events such as charity basketball games or cooking events for people to visit. A number of members also use the term Nupe when referring to previous members that they hold in high esteem.