I'm by no means an expert, but here's my shot at explaining these terms for you:

fun fly: an airplane that is designed to be able to perform extremely radical maneuvers, like flying 4-foot diameter loops, rolling 720 degrees per second, etc. These are usually very short-bodied, fat-winged, with very deep chord, and don't look like any "real" airplane you ever saw. Some make the attempt, like the Sig Somethin Extra, but they really don't.

Sports model: an airplane that is designed to be fairly easy to fly, yet quite aerobatic, and that also "looks good" - ie, resembles some "real" aircraft. Examples might be - Great Planes Sportster series, Sig 4-star series, etc. Usually, but not always, low-wing rather than high-wing.

Scale model: an airplane that is as close a possible to an accurate miniature replica of a "real" aircraft - for scale competition, these are also usually accompanied by some sort of documentation proving the exactness of the replica. The most popular of these are warbirds (P51, P39, F4U, etc.) and international aerobatic competition aircraft (Extra 300 series and derivatives, Staudacher, Edge 540, Laser, etc.)

racing model: aircraft that are designed for one purpose only: going extremely fast in a quite small oval pattern. "go fast, turn left!" Some are modelled after actual Reno racers - one of the more popular is the many modifications on the P51 Mustang, and the purpose-built racers like the Shoestring, etc.

stunt model: a term used to describe almost any R/C aircraft that is capable of aerobatic performance - more descriptive of the way the aircraft is flown than of the aircraft itself. Can be applied to any "sports" model, most "scale" models, all "3d" models, etc. An aircraft you can do stunts with.

3d plane - aircraft that are designed to perform radical manuevers like hovering (hanging still on the prop), and other seemingly impossible manuevers. The majority of these tend to be very large aircraft - 27% and larger scale models of international aerobatics aircraft, and very, very overpowered. These aircraft fly 'normally' at 1/4 throttle, and hover at 1/2 throttle or less.

Pylon racer - see "racing model", above.

Hope this helps, and hope I got it right.