CM,
From an unreliable and dated memory, the alerting levels CAUTION TERRAIN, and TERRAIN AHEAD might be the difference in the mechanism of alerting. The first based on radio altitude (as original GPWS), and the second by position comparison with the terrain data base - EGPWS.
Both mechanisms are within EGPWS, possible retained for positional error / map slip / nav failure - the system reverting to basic modes.
Selection in Airbus, if still relevant, could inhibit position input (TERR OFF ?). **
The OBSTACLE calls only apply to EGPWS, and only with operator system configuration.
If both calls are at the alert level -
amber, possibly the difference in being above the obstacle height and below it. Or if the second call is at the warning level -
red, it might proceed a Pull Up.
sonicbum, from the above, the EASA view appears to represent EGPWS operations, and the FAA, previous GPWS installation, being unable to look ahead like EGPWS.
** referred to in incident #8 (TERR OFF) - read in full for lessons learnt.
https://www.icao.int/safety/fsix/Lib...plus%20add.pdf
CAUTION The above is based on an old and fragile memory.