GPS is ground speed, so it is influenced by the wind and is not a measure of airspeed. With a low stall speed and strong wind, you can fly with GPS speed of zero.
TAS is the actual speed you are travelling through the air, i.e. the speed someone in a balloon floating with the wind with a radar gun would measure.
IAS is indicated airspeed, the speed that is shown on the airspeed indicator.
CAS is calibrated airspeed, which is what a perfect airspeed indication system would show. Airspeed indication systems are not perfect. IAS and CAS should be very close at cruise speed, but IAS often has large errors at high angle of attack, i.e. close to the stall.
IAS and CAS reduce approximately 2% per thousand feet due to reduced air density. Aerodynamic loads e.g. lift are relative to CAS so we can use indicated airspeeds for stall speed, approach speed etc.
Vne could be limited by aerodynamic loads, or it could be limited by flutter. Aerodynamic loads are related IAS(CAS) but flutter is relative to TAS.
Typically, small aircraft have a limited service ceiling, so if the ceiling is 14000 and VNE is 130 knots they might test for flutter to 190 TAS and just give the one number 130 IAS. If an aircraft has a higher ceiling e.g. gliders where altitude is not limited by the reducing engine power, VNE can be TAS or can change as altitude increases.
The biggest problem is e.g. experimental aircraft where people put a big engine in that allows it to go faster and higher. The spread between IAS and TAS can be bigger than was assumed when the Vne was set originally, so you can reach a higher TAS than it's designed for.
Summary:
Certified aircraft: Vne is whatever it says in the POH. Could be IAS, could be TAS or IAS changing with altitude.
Non-certified: There's no guarantee how Vne was tested. It is conservative to assume TAS, particularly if it has a larger engine than the original design.