1. 3D flying is one style of aerobatic flying. 3D planes do a lot of flying while stalled (the wing is not "flying") like hovering, torque rolls, upward spins, all sorts of funny flips and spins. More traditional aerobatic competition (Pattern or F3A) is more about precision: straight lines, really round loops, etc. Almost any plane can do some aerobatics but might not be competitive at high levels.

2. Sport Flying... there was a long thread to define this ... I'd say it is flying without any competitive goals. The planes are more geared towards everyday usability than performance in some specific area.

3. Profile planes have very simple fuselages. Basically a profile plank, instead of three dimensional.

4. Fun fly planes are a lot like 3D, as far as I can tell. More skinny fuselages, I think.

5. Pylon racers are used to race around pylons. There are several different classes, some mandate boxy fuselages, some require distant resemblance to full size planes, some just give a few measurements to limit the design.

6. Extreme speed... some planes are good for going fast, some will not go fast whatever engine you put on. Engines do make a difference too.