Ok you're right those names like "ascended ssj" and all that are made up by fans to make sense of it all.
I still disagree with the Vegeta training thing, after the Frieza saga he nearly killed himself to become an ssj. He busted his ass for 2 years in that chamber to get stronger, and he became ssj2 on his own without having a deadly foe to push him or being in other world like Gohan and Goku had. All Vegeta did was train, Bulma even said it herself, that's all he does it train. She said that when Gohan was grown and went to visit at the beginning of the Buu saga. So Vegeta trains just as hard if not harder than Goku, I mean how the hell else is he gonna keep up without the natural talent, and without all the other world/heaven/king kai benefits?
Also you're wrong that Goku was ssj2 before the end of the Cell saga, he wasn't an ssj2. Goku didn't reach ssj2 until after the Cell saga like Vegeta, but you are correct that Gohan reached that level against Cell. Also, not only did Gohan's power level stop growing after the Cell saga, it went down a lot.