Hi michelda,
Gps approach = Approach using GPS satellites position updating (uses the USA System of Global Positioning Satellites)
Gnss approach = Approach using Global Navigation Satellite System (can use present GPS and the new European Galileo Sat Nav System of the future) (eg GNSS APP LGW 26L required accuracy = 0.3nm)
Rnp approach = Area Nav Approach using DME/DME, VOR/DME, or Satellite system for position updating with a position accuracy of "X". (X is usually 1 nm)
Rnav approach = Area Nav Approach as above - but not necessarily to the same required accuracy
Rnp ar approach = Not certain - think it might be the Arrival Procedure leading to the RNAV Approach.