97-03 model water pumps have the thermostat as part of the thermostat housing, and is not removable (at least not by hand). This style uses a large O-ring to seal the housing to the pump. 2004-2008 water pumps have a thermostat that has a separate housing, and the thermostat easily slides out. The O-ring on this model is part of the thermostat. Another visual difference is in the casting. The 97-03 housings have an additional tab on it to hold the wiring in place for the A/C compressor. The 2004-2008 models do not have that tab. The housings are not interchangeable between pumps since the diameter of the thermostat cavity is different and the bolt pattern for the housing is different.
NOTE: GM water pumps sold after 2005 all have the 2-piece design, meaning if you ordered a new GM water pump for your 1998 Corvette, it came with the newer 2-piece thermostat.