As you deduced, 6e is a marketing term that was used before the formal adoption of 6a. To correct the term, lets call it enhanced Category 6. The "things" in question that have been modified generally have to do with the physical characteristics i.e. number of twists per inch, separation of pairs and the existence/type of shielding on the cable.
The question isn't really whether 6 vs enhanced 6 vs 6a will -support- 10GBaseT, but rather at what distance. Cat6 is officially rated to go to 55M (including patches) while 6a is good for the full 100 meters/328 feet. This isn't to say, of course, that a 75M run of cat6 won't work - just that it's outside of TIA spec.
Here's the thing, though - if the 5e / enhanced 6 / 6A wasn't correctly terminated on compliant patch panels/connectors/jacks then none of this actually matters all that much. Enhanced 6 should exceed 6 and may be equal to 6A, but the lack of an official spec at the time basically means that you need to base your design on the results of certification with a cable tester capable of measuring to these kinds of speeds. If you can hit 500MHz at the right crosstalk and such (as per 6A) then you're good. If not, then your cable vendor owes you a re-run.