As I understand it. GNSS is satellite navigation, it includes the American system (GPS), the Russian system (GLOSNASS), and any other systems that might be used. Therefore "GPS" is an outdated term as it excludes other satellite nav systems. Chart names have progressively been changed from RNAV (GPS) to RNAV (GNSS). So for practical purposes RNAV (GPS) is exactly the same as RNAV (GNSS). RNAV (RNP) refers to approaches that require a certain navigation performance but it doesn't matter how that performance is achieved, whether it be GNSS, VOR/DME, INS etc. In an RNP approach you could lose the GNSS nav solution (RAIM) and continue the approach provided your box is still providing you with the required navigation performance.
As I say, that's my understanding, but it's not exactly my strong point. I might understand it better if our company did RNP approaches but we only do RNAV(GNSS).