Hi 9MM,
Kitesurfing - Riding waves on either twin tip or surfboard.
Kiteboarding;-
Freeriding - Just riding around having general fun
Freestyling - Old School - Big Boosts, board offs, rolls and anything huge!
Freestyling - Wake Style - Wake type tricks generally with kite lower than 45 deg.
Freestyle - New School - Large kite loops with handle passes and advanced wake style
Slalom and Race - Slalom and racing around buoys
Kite cross - racing around floating obstacles
Kite Park riding - Sliders, kickers and other apparatus
Kook Style - Having no lessons, crashing on launch, kareening off out of control taking out others and then smashing the kite on the beach after draggging through the red/yellow flags on the surf beaches. Most often whilst wearing a seat harness, helmet, impact vest, Reel leash and flying a very old kite with no safety and having a couple of laughing clueless buddies in tow.

Hope this makes sense. Good winds,