confusion between RNAV and RNP approaches and specifiations
RNAV was/is in the older model where each approach was designed around a specific technology, and any detected failure to meet the (assumed) fixed accuracy of that technology means you can't use the approach at all.

RNP is newer ICAO terminology under their Performance Based Navigation model, which essentially means they don't care how you get your navigation data, just how accurate it is.  The better your Actual Navigation Performance is (i.e. lower number), the lower the approach minimums you get to use.

TSO C129/C196 systems cannot be used as the sole navigation equipment because it only has fault detection, not fault exclusion; if the RAIM detects a fault, you have to stop using it and switch to something else.  (If you don't have RAIM, you have to actively cross-check the GPS, so you might as well just use the other system as primary.)  Notice the parallels to the explanation of RNAV above.

TSO C145/C146 do have fault exclusion, so they can be used as the sole means.  They also support SBAS (aka WAAS), which can offer much lower approach minima where available, but they will gracefully degrade to higher minima depending on the signal accuracy--which can vary over both space and time for the same equipment.  Notice the parallels to the explanation of RNP above.