In the old days, if you had the required equipment you could fly in a given airspace. This was specified in ICAO annexes and regional supplementary procedures, etc... This is, I understand, equipment based navigation.
Nowadays, if your equipment, whatever equipment you have as long as it is approved, meets the required navigation performance of a given airspace, then you can fly in it. This is, as opposed to the above, performance based navigation.
The NAT MNPS is a similar thing, a precursor of RNAV-RNP.
The implementation of RNAV-RNP is being progressive. It started with BRNAV, later with PRNAV. But I thought that these would both superseded by RNAV-RNP with RNP 5 and RNP 1.
But who cares! The goddamned FMS will get us where we want no matter what ICAO docs, leaflets etc they may print. I am going to drown in a sea of paper, aaaaaaaaagh