I think it goes like this.
The dragon is g6 on move 5
The accelerated dragon is g6 on move 4
The hyper-accelerated dragon is g6 on move 2
I don't know much about this but... I think the accelerated and hyper-accelerated aren't as good because they aren't as flexible and cut out some good alternatives for black depending on white's moves.
OTOH they're popular for club players due to some trappy lines and because there are less transpositions you need less book knowledge. The idea of leaving the quarter of a pawn advantages for the GMs to sweat out.
As black Najdorf or Dragon and sometimes Kan when I'm bored
As white against:
Najdorf: Bg5 or Rg1 when looking to play something different
Dragon: Yugoslav attack
Acclerated dragon: Marcozy Bind
Kan: Same as above
Taimanov: same as above
Schevigenen: Keres Attack
Classical: Rich Rautzer