Physical channeling is the act of adopting some aspect of an element to increase the abilities of the fighter above and beyond what is possible for humans. In addition their talents allow them to use weapons that would be impossible for normal humans. For example Ulrick has superhuman strength and speed from his connection to water, and his axe is actually formed from a slow moving liquid allowing him to alter its density, hardness and shape at will. In addition if a large amount of power is channeled the subject can enter an altered state. Once again the example from the comic would be Ulrick, who uses the power of water to enter a clear trance where his only goal is to destroy his enemies. This berserker state also increases his speed, strength and technique.
Direct force manipulation is the creation, alteration and wielding of the element that the subject has an affinity for. The most common use for those techniques are to throw said element in such a fashion that the target is hurt by it. Hikaru is a master of this. However there are many other things that can be done by elemental control. Other then the obvious advantages of being able to control or alter an element to ones whim elemental magic can be put to a number of other uses some of which do not exactly seem plausible. For example an air mage could learn to use the wind to fly. Or that same mage could cause the air to show false images to her foes. The elemental forces are powerful and mysterious.
'True' magic is the most varied of the three disciplines. Anyone can learn this magic, though the study of it is fairly difficult. Once again strength in this magic lies in the bloodlines of the wielder, but unlike elemental magic it seems only random chance determines who can truly master the art and who will merely be an adept. 'True' magic allows the caster to see across great distances, alter the minds of men subtlety and wield all the elements, admittedly at a minor level.