http://crystalhall.wikia.com/wiki/Whateley_Academy_Wiki

Exemplar is a Whateley specific term, for one specific mutant trait... or power, if you prefer.

Brick is a more generic comic book/superhero genre term. The common terms are:

Brick - typically invulnerable or capable of taking a lot of beating to bring them down.
Blaster - someone that uses ranged attacks (often energy beams) to cause damage
Scrapper - melee fighter
Controller - use various methods to control where the fight happens and who can engage who
Supporter - boost ally abilities or reduce the effectiveness of opponent abilities.

These generally correspond to the standard gaming roles of: Tank, Ranged DPS, Melee DPS, Crowd Control, Heals/Buffer.

The Whateley traits are more specific to how a given power works than about how it is used. A given trait might produce specific powers that would allow the mutant to fill one or more of these roles, while another mutant with the same trait might be completely useless it.

Exemplar is the basic evolutionary upgrade. Mutants with the trait are generally stronger, faster, smarter, have better reflexes and so forth. Sometimes the trait is limited and they aren't improved in all areas, and often being Exemplar means that the mutant has a BIT (Body Image Template). A BIT is a psychologically imposed blueprint on what their body 'should' look like, a sort of 'ideal' that they adapt to. It's a little more complicated than that, but that's close enough for a basic understanding of Exemplars.

Psychokinetics / PK is a mutant that projects a shell (force field) around their body that protects them and allows them to interact with objects as though they were significantly stronger than their physical body is.

Energizers run a wide gambit of results, but they are basically mutants who generate or transfer energy from outside our dimension into doing 'something' ... where that something can range from energy beams to speeding up their actions to supercharging their body.

Wizards have a natural affinity for magic, naturally drawing it to themselves for use. It's important to note that in the WU, ANYONE can learn spells and perform magic... if they train to do so and have access to a source of magical essence. However, few people have the ability to focus well enough to avoid wasting what they get if they do get essence ... or are likely to be gifted enough essence to kickstart the process of development to get more. Mutants with the wizard trait bypass a lot of the hard work needed because they just automatically have a source of essence flowing into them... so they don't have to worry about the magical equivalent of buying batteries or keeping them charged.

Avatars are mutants that have a part of their natural make-up that makes them able to host a spirit. Spirits (like totem animals or elementals) require safety and an energy source to survive in our dimension, Avatars provide this. In exchange, the bond (or symbiosis) allows the spirit to grant the mutant some abilities relevant to its nature.

Channelers and Paladin are subsets of the avatar trait, each allowing a bond with spirits or divine beings far beyond their ability to 'host' ... they are fairly rare in the WU, though not necessarily as rare in the stories (especially fan fiction).

PSI - various psychic abilities can be found in mutants. The most common are Telepathy, Empathy, and Telekinesis. There are also Precogs, Psychometrists, Clairvoyants and so forth. One interesting type of PSI that often gets named uniquely rather than being called a PSI ability is the Paragon trait (which allows the mutant to instinctively grasp any skill they apply themselves to, quickly growing in skill until mastery).

Gadgeteer/Devisor - these are the inventor traits. The difference is often expressed as "the Gadgeteer can be found in the Patent office... the Devisor anywhere but." This refers to the nature of the 'science' used by the two. A Gadgeteer might make something that is generations ahead of our current technology... but if explained and taken apart, could be built by anyone else with the equipment to make it. Thus, the inventions of a gadgeteer can be patented. A Devisor, on the other hand, doesn't necessarily limit themselves to the laws of physics. or mathematics. or... well, anything really. As such, their equipment may not work for everyone. It may not work reliably at all. But it also may do things so far beyond what is expected to be possible using the given materials that no one would have believed it possible. Mad science is what devisors do. And no one can take apart what they've done and reproduce it. Generally (some other mutants might have powers that allows them to do so, but no normal human could).

Shifters - change shape, obviously. Power mimics also tend to fall under the Shifter ability (adjusting the body to produce different powers requires some shifting).

Regeneration - self healing at an extemely high pace. Note that Exemplar tend to have Regen a couple levels below their Regen ability by default.

Warpers - alter the basic rules of physics around them. These are your 'luck' specialists (probability warpers), teleporters, density changers, size changers and so on.

That's the bulk of it. There are names for some sub-categories and more rare traits, but the important thing to remember about traits and rankings in the Whateley Universe is that they are named/designed by researchers and lab types who are trying to categorize and understand how mutants evolve to do certain things. As such, the traits and numerical rankings don't necessarily work as a clear means of comparing two mutants. An Exemplar 3, a PK 3, an Energizer 3, a Wizard 3, a Gadgeteer 3 and a Shifter 3 are not going to be able to pair off and have 3 relatively even sparring matches. Those 3 rankings mean very different things within the given trait.