From Diablo Wiki
A spell is a a magical incantation. In Diablo III all spells are counted as skills, but all skills are not spells.
Diablo III Spells
Your character employs a variety of skills and spells that you activate by using the left and right mouse buttons. You can change which skill or spell is associated with either mouse button by left-clicking on the Left or Right Action Icons.
Left-clicking on these icons brings up a menu of all the possible skills and spells for that mouse button. While all active skills are available on the right mouse button, only direct attack skills are available on the left. Which skills are available on the left and right Action Icons depends on the class of character you are playing. As your character learns new skills, they appear in these menus.
Nature of Magic
Magic is an extremely powerful force, the manipulation of which is carefully studied, frequently learned, but it is never fully mastered. Enchantments exude an aura that can be sensed by many, but years of training are required to properly exploit the Mana that pervades our world.
Some scholars use natural manifestations to explain the workings of the universe. In a common archetype, the physical world is likened to the sky while the ethereal realm of magic is set as the ocean. If we follow this line of thought, spells are much like the turbulence that occurs where the two interact with each other. During the Sin War, Demon and Angel alike wrought powerful magicks that threatened to tear the fabric of reality apart. The physical and magical realms began to blur and merge, which, in our archetype, would be the equivalent of a fierce hurricane.
The Forces of Order sought to preserve our reality by limiting the power of mortal man. As a consequence, only the strongest wills can harness more than the most basic of magical effects. Even then, much energy is lost in the transition of power between the two Realms. As a practitioner of the arcane arts grows more knowledgeable he is able to create these effects with greater efficiency, resulting in spells that are more potent, have more endurance and drain less Mana in their casting.