Have only just had a quick scan of this thread so apologies if somebody has already said this but .............
A, AA, AAA was (at one time) a standard accepted as separating the quality of Tanzanite. AAAA was purely a GemsTV category and in actual fact meant nothing at all. All it meant was that GemsTV felt is was the better of all the Tanzanite they had and was top quality. In the old days, that was probably true.
Majestic is just a re-branding of the AAAA category because I think there was a move away in the industry from using confusing terminology and GemsTV have applied that to other gemstones such as Emerald, Ruby etc etc
I believe that Tanzanite is going to be graded in a very similar way to other gemstones and the A, AA blah blah blah won't be used. It was probably this change that prompted GemsTV to change their grading but I don't know that for sure.
Basically, buy with your eyes. If the colour is a top colour it'll blow your socks off IRL. It'll be either a pure blue, a blue/violet (although as a descriptor that's misleading because blue/purple would be more accurate and vice versa as purple/blue. It'll be a deep colour that you can't see through, vibrant and yummy!
Hope that helps.