Natural magic is the most basic forms of the arcane arts. It is the first type of magic that anyone learns to use. Natural magics are also the weakest in form, but take up the least amount of a person's energy. Natural magic exists in all elemental things. This form of magic is also the most tactile and is dependent upon the items being used in order to work. Basically this means you cannot create anything out of nothing. Fire is the only element that appears to just be created when in reality it is caused by the magic user heating up the air around their hand or an object until it combusts.
Elemental magic is a type of Natural magic. As the name would have you believe elemental magic deals with, you guessed it, the elements. There are four natural elements: Earth, Fire, Water, and Air. Ice and metal are both different forms of the earth and water elements and thus exist as a part of that element.
Vegetative magic deals with the controlling and manipulating of plant life.