Do Airbus actually recognize these designations?
Airbus yes, EASA/FAA/JAA on the other hand dont as this is purely a commercial/marketing designation.
Now to clear it up,
The X designator came to the A330-300 when the 230-233t weight variants were first offered. No X for the -200
The A340-300 received the X designator when the 271-275t weight variants were offered.
The E designator was applied to A330-300 when the following enhancements from the 340-500/600 became standard on the A330.
GPCU/AGCU combined to a single GAPCU
Mechanical link to rudder replaced with a electrical signal and some control logic changes similar to A340-500/600
Speed brake can be used with all flap settings
Auto start of one of the electric hydraulic pumps to assist with rudder control under some failure conditions
LCD screens as per the A340-500/600 and newer A320s.
EGPWS mode upgrades and a new peak terrain function
ISIS standby AH with inbuilt bugs and ILS receiver as found on newer A320s and A340-500/600
Backup Speed Scale / Altitude Scale in the case of all 3 ADR being turned off or for invalid data (e,g, ADR probe faulty)
New data loader
The A340-300 also received the E designator when the same enhancements as mentioned became standard including the new CFM56-5C4/P*
A340-500/600 also received the X designator eventually after the HGW weight variants were offered.
P as in PiP a.k.a. performance improvement package.
To sum of the french logic.
X = Increased gross weight
E = Enhanced