As the Sorcerer, the Wizard uses changes in the environment to shape their reality. The difference is the energies used and the method they are employed. Instead of forcing their will on the environment, the wizard takes a more scientific edge to their use of power and examines the intrinsics of the interactions between the Astral Plane and this plane. Instead of creating changes and making things bend to them, they take normal physical circumstances and try to work within those confines using a magical touch. Things that already exist will simply be given a magical “spin” and be allowed to continue by altering their astral form, thus making all the magics of a Wizard seem odd but natural. If a ball would normally roll straight, the Wizard would only make the ball veer left or right, not stop it in motion or whatnot.
This extremely coy and natural form of mystic power is truly the spirit of “occult”.