The most significant cause of the discrepancy is probably the temperature difference from the International Standard Atmosphere. When the temperature rises the air expands and the Flight Levels will rise higher above the earth. Although 2000 ft seems a lot, it's not uncommon.
My rule of thumb is 0.35% per degC mean deviation from ISA. So for a 2000 ft difference at 40000 ft, that's about ISA+15 degC if it's all temperature error. If the QNH is 1033 hPa, that's worth 600 ft feet on top of an altimeter set to 1013, so it could be a little of each.
if you are displaying WGS84 coordinates on your GPS the GPS height will be the height above the WGS84 reference ellipsoid,
But
do common aviation GPSs display HAE for "altitude"? Given that other elevations (e.g. terrain and obstacles) are referenced to mean sea level, it seems strange that GPS manufacturer would choose to ignore a relatively simple correction like geoid height.
The GNS430 manual for example says:
"The altitude calculated by GNS 430 GPS receivers is geometric height
above Mean Sea Level and could vary significantly from the altitude displayed by pressure altimeters in aircraft." (my
italics) It doesn't say "above the WGS-84 reference ellipsoid".