Exactly. The approach path is constructed entirely within the FMC, all the ground station does is transmit a correction signal to the aircraft's GPS system, such that its accuracy is improved to an appropriate level.
Not true for GLS approaches. The approach that is used by the autoflight system is not database dependent, it is information send by the ground station which provides the approach and correction data. Without the correct approach geometry data (selected via the channel number in the nav receiver and then received from the ground station) you can have the GLS approach in the FMC and still not fly it.
The article linked in by Avenger is actually very very clear on that subject:
Each approach is given a unique identifier for a particular FAS, glideslope, and missed approach combination. FAS data for all approaches supported by the particular GBAS facility are transmitted to the airplane through the same high-integrity data link as the satellite range correction data (i.e., through the VDB data link). The MMRs process the pseudorange correction and FAS data to produce an ILS-like deviation indication from the final approach path. These deviations are then displayed on the pilot’s flight instruments (e.g., Primary Flight Display [PFD] ) and are used by airplane systems such as the flight guidance system (e.g., autopilot and flight director) for landing guidance.
To fly the approach all you need is the MMR, not the FMC. The approach selection in the FMC serves only the same purpose as the approach selection for an ILS. It displays it on the ND, but is not the source of navigation data used by aircraft systems except for use as an overlay approach.
The article goes on about two different selection methods, however the FMC based selection method is not approved and supported in current operational 737 GLS installations, only selection via the NAV-panel directly into the MMR is supported. However if the approach is coded into the FMC it will show the channel number (but not select it) same as it would show (but not tune) the ILS frequency for an ILS approach.
This is in line with the rest of the 737 NAV interface which does not support auto-tuning, unlike other boeing airplanes.
By the way, thanks a lot for that artice, although it was written during the prototype phase of implementing GLS approaches it explains quite a lot.