Ive been really confused between these two specifications recently. For example my research suggested that RNP has on board monitoring and alerting and RNAV doesn't require this, however then why must we compute a RAIM check before conducting an RNAV app when for RNAV specification no alerting or failure detection is required and hence TSO 129 may be used? Also doing my flying in Australia some ADs would state there is an RNAV app available for one runway and also an RNP, what additional requirements would there be in terms of pilot training or alerting etc for the RNP app. Appreciate all answers just trying to get a grip with this confusing concept!
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.