The following is a conversation you can hold with Raya-O-Senna following the level 60 WHM quest. (No worries, no spoilers). It details the advent of the Black and White Magic schools, though what schools of magic may have existed before this time, I cannot say; but it's fair to assume that certain techniques may have been lost and rediscovered many times over the eras.
What is White Magic?
A curious question from one who has borne witness to the tragedy of Amdapor with her own eyes. What is white magic, indeed? Very well. I shall give you my answer, that you might judge for yourself how it compares to your own.
The art now known as white magic dates back to the Fifth Astral Era. It was then that a brilliant young sorceress─for the first time in history─succeeded in channeling not merely her own life energy, but the aether that inhabits the very land itself. Her magic was that of destruction: black magic. The people of Amdapor felt this power was too great to be allowed to go unchecked, and so it was that white magic─the magic of healing and solace─was born. So it was that the forces of magic were brought into equilibrium, and civilization flourished. But this era of peace and prosperity would prove short-lived. War broke out, and the realm was thrown into chaos. The War of the Magi. To rain death and destruction on their foes, mages summoned forth greater and greater powers. The war raged on, until the aether dried, and the land itself could bear the burden no longer. So did the hubris of magi bring forth the Sixth Umbral Era...and with it a mighty flood that swept away entire civilizations, leaving naught but ruin and suffering in its wake. The survivors─what few there were─banded together. Vowing never again to repeat their mistake, white and black magic were declared forbidden arts, never to be practiced again. The elementals of the forest, knowing that men could not be trusted to keep such vows, took action as well. The Twelveswood grew, swallowing the ruins of Amdapor, and the power of white magic was sealed away deep in the forest, far from the reach of mortals. Ages passed, until five centuries ago, the elementals at long last welcomed people back into the forest. So the nation of Gridania was founded, and my people─the Padjal─came into being, to serve as mediators between elementals and those who would reside in their forest home. It is from the elementals themselves that we inherited white magic.
In any case, living beings generate aetheric energy as a natural byproduct, the excess bleeding off into the environment, and still larger chunks dispersing into the flow of the Lifestream, generating currents and forming deposits of crystals and ceruleum. The pure energy can take on different elemental aspects, almost like a "flavor", but at the basic levels it is all the same: it is just easier for aspected aether to manipulate its prospective element. That being said, I don't think that when you use a spell, that you are creating that phenomena from pure energy; instead you are using that energy to effect the phenomena from already present components (condensing water from humidity in the atmosphere, building a voltage between two points to create lightning).
Though yes, in-game play ignores the fact that there's probably not any rocks for a white mage to use on a boat out at sea. Compromises.
Though I do still get peeved when something major happens (like a major character being badly injured or killed), and I as a White Mage can't use Revive or Benediction on them when I CAN CLEARLY STILL SAVE THEM.