In the instance that I checked it, it said "SBAS PA". The flight manual said that it can operate in "SBAS" as well, leading me to believe that there is a difference between the two. The flight manual said nothing else on the subject of the different modes, and a Google search didn't turn up anything. Is there any documentation on GNSS receivers having these two different SBAS modes?
SBAS PA = Precision approach. Navigation integrity is assured by a satellite-based monitoring system like the WAAS system, and the monitoring meets requirements for SBAS approaches (LPV) as described by RTCA/DO-229.
SBAS = Integrity is assured by a satellite-based monitoring system, but doesn't meet RTCA/DO-229 requirements for precision approaches. You'll have to stick to more traditional approach types.
I'm honestly not sure when plain "SBAS" mode applies, and my GPS manual doesn't provide much clarification. It could be your procedure isn't loaded or hasn't gotten all the information it needs like the FAS block. It could be when you're outside the precision approach region, or outside the service area for the satellites even though you can see the satellite, which is pretty common but I think you shouldn't even be in SBAS in that case. It could even be the case that there are SBAS satellites that support position corrections but not approaches - I don't think as of this writing that Japan's MSAS supports LPV.
The difference in your Collins FMS between the "SBAS" and the "SBAS PA Mode" appears to be, in the "SBAS" mode, the absence of SBAS-aided positioning. When in the SBAS PA mode all WAAS corrections (fast, long term, and ionospheric) are available.
The National Satellite Test Bed defines the "PA Approach Navigation Mode," with respect to WAAS as:
(highlighting and emphasis are mine)
Here is a Multidisciplinary Digital Publishing Institute (MDPI) article (Abstract) discussing SBAS-Aided GPS Positioning with an Extended Ionosphere Map at the Boundaries of WAAS Service Area . In this Abstract, in section 2.1 you can note that the distinction between "PA Mode" and "NPA Mode" is the absence of ionospheric corrections:
(Highlighting and emphasis is mine)
The third paragraph, last 3 sentences of section 2.1 in the Abstract noted and linked above state:
If neither PA or NPA is available, GPS-only positioning is enabled. At the boundary of the SBAS service area, only a part of the satellites has the full corrections. In general, the orbit/clock corrections are available but the ionosphere correction is not available at the boundary.
This is why I believe that if only "SBAS" is displayed, SBAS-aided positioning is not available.
(emphasis is mine)