i see them in the titles of some fo the runs, and also turbo.

obviously i'm a noob.

can some please help me and explain these two things for me.

thanks

Boosters = Modifiers such as speedup, dealing 9999 with every hit, etc. These are only available on the HD releases.

Turbo = A turbo controller, which in most speedrun communities is not allowed. For FF9 we do have a console leaderboard that allows it, as well as allowing it generally on the HD version.