Theurgy, thaumaturgy and goetia
Three old terms sorting magic by aim: theurgy seeks union with the divine, thaumaturgy works wonders, goetia deals with spirits.
Also: theurgy, thaumaturgy, goetia, high magic, wonder-working
Theurgy, from Greek theourgia, divine work, was used by Neoplatonists such as Iamblichus for rites meant to draw the soul toward the gods. Thaumaturgy, from Greek for wonder-working, names the performance of marvels, and is applied to saints as well as magicians. Goetia, from Greek goes, a wailer or sorcerer, came to mean the calling of spirits, and gave its name to the first book of the Lesser Key of Solomon. Renaissance writers ranked them as high, middle and low magic. The scheme reflects a view from learned circles and does not map neatly onto what practitioners do. Modern ceremonial magicians use the terms in their own ways.