I'd like to learn the speedrun of this game, but I don't know why there is different categories of consoles. Is there some glitch making the version different or is it just to make load times fair between leaderboards? I guess it would be the 2nd option, but can someone confirm this?

Yes it is just to make things fair. As far as I know, mostly every game splits categories between consoles, and the Final Fantasy series games that are available on multiple consoles are split like this as well.