The terrain data is contained in a database within the EGPWS (Honeywell TM) or the Terrain Awareness and Warning System (TAWS) as defined in the regulations -- can't use a trademark in the regs.
The discussion in your link about "blockiness" when zooming in is a result of the database grid references. To save memory space, the resolution of the world-wide terrain data varies based on terrain variation and it's relative hazard to flight operation. There's greater resolution (smaller grid) near airports and in mountainous areas.
The A320 does have airborne radar that is capable of displaying "weather" which really means precipitation. It can't be displayed at the same time as the terrain to avoid confusion.
Neither the EGPWS or the radar data are in the FMGS. Their data is just underlayed on the navigation display. (EGPWS does receive data from the FMGS to support it's warning functions.)
TAWS/EGPWS function is described in TSO-C151c