A guy could write a book on the topic you've brought up. Actually, to do it right, many books. But I'll attempt to give you enough information to make sense out of the vast array of planes. I like to think of them in classes or performance levels.

1. Trainers
Lots of self-righting characteristics designed into the aerodynamics of the airframe, small control surfaces to make them less sensitive, and little to no consideration given to aerobatic performance. Every compromise in performance (speed, maneuverability, and neutrality) has been made to improve straight and level flight and to create a model that's forgiving of bad piloting.

2. Aerobatics trainers/ 2nd airplanes/ Sport planes
Most or all self-righting characteristics removed from trainers to improve overall performance, and generally bigger control surfaces for more maneuverability. They still are designed to be stable in straight and level flight, and stall resistant airfoil and wing shapes are still used to still be forgiving of bad piloting. These planes are the ones you see everywhere- the Ugly Sticks, 4 Stars, etc. If you can fly a trainer around the circuit and land without having to make big corrections, you can fly one of these planes. Most pilots comment that these actually are easier to control than their trainers were due to the better overall aerodynamics that are possible without all the self-righting characteristics.

3. Fully Aerobatic planes
Very little consideration is given to making these planes forgiving of bad piloting and there are no self-righting or stability characteristics designed into the aerodynamics. Pilots say they fly like they are on rails, because when set up right they do exactly what the pilot tells them to do and nothing else. That can get a new pilot in trouble, because there is no roll or pitch coupling to prevent stalls. Airfoils and wing shapes are designed to stall on demand for certain maneuvers. But poor piloting can bring about stalls unexpectedly, which can cause a crash quickly. These planes are for pilots who can already fly aerobatic routines on a sport plane and want to improve their performance. Examples include all competitive aerobatics planes- IMAC, F3A, SPA, etc. The specific competitive division's rules dictate which designs are legal. For example, IMAC requires scale models be used, whereas F3A allows nearly any design so their planes don't have full sized equivalents. Specific examples would include the Yak 54, Edge and Extra series, and the Kaos.

4. 3D and Fun Fly planes
These are similar to aerobatics planes, but have bigger control surfaces, more stall-resistant airfoils, and higher power to weight ratios. They are purpose built for doing stunts at low speeds, many of them done using only prop wash for lift. These overlap with sport planes and aerobatics planes in use, because some are very easy to fly with lower control throws. The H9 Pulse is a good example of an overlapping design.

5. Racers
Every design compromise has been made to improve high speed performance. They have thin airfoils, small fuselages and tails, and small control surfaces compared to sport models. Most can't do aerobatics and the thin wings are prone to stalling at lower speeds. You have to have good orientation skills and quick reflexes to fly these, and you have to be good at landings to keep from stalling them.

6. Scale models
These can fit into any of the above categories, just as their full size equivalents do. As the name implies, scale models are copies of real airplanes. Because the air works on a model differently than on a full size plane, scale models don't generally perform as well as a similar plane that was originally designed as a model. That's why many popular scale models come with the warning that they are not for beginners, especially WW1 and WW2 fighters.

Does that get you started?