Real training = meeting disney characters and whacking heartless to death until you unlock more abilities to whack bigger heartless to death
Fake training = sparring with another keyblade wielder, listening to the wizard, eating ice cream in the void
For real, if Sora and Riku are the top dogs despite literally only ever screwing around and getting themselves into trouble, then what use is hanging out at the "home base" and training? Kairi really should have just snuck off with Donald and Goofy to look for Sora behind the wizard's back, it'd be more in line with her character.