West Coast,
I think it is safe to consider them two independent systems, even if they are isolated through electronic logics inside the same box. The reason is that the 737 MEL has the following separate items:
Ground Proximity Warning System (TAWS)
1) Modes 1 thru 4
"May be inoperative for a maximum of 6 flights or 25 flight hours or 2 calendar days, whichever occurs first."
4) Terrain Awareness & Warning System (TAWS) May be inoperative for a maximum of 10 calendar days provided the GPWS functions are operative.
and
5) Terrain System – Forward Looking Terrain Avoidance (FLTA) and Premature Descent Alert (PDA) Function May be inoperative provided alternate procedures are established and used.
Glideslope, windsheer, and advisory callouts have separate items too. Probably as the box is able to isolate each mode if a sensor input is missing, instead of rendering the entire GPWS inoperable.
I don't know what you think about the reliability of the following source, but as you can see, they list terrain proximity as a "not numbered mode" (scroll 2/3 down):
SKYbrary - Terrain Avoidance and Warning System (TAWS)
On another note, some years ago a friend on mine landed on a newly built runway that wasn't in the TAWS database. Since the new runway was at a considerable distance from the old one, he got "TOO LOW, TERRAIN" warning during approach. Clearly a TAWS function (descent below unsafe radio altitude while too far from any airport in the terrain database), because no mode 1-4 would have been triggered during a normal stabile approach. So this is an example of how it works in practice.