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Genie is a hypernym used to refer to the inhabitants of the elemental planes of the forces of nature: Earth, Air, Water, Fire. The genies can be divided according to those four Principles:

The priest Krepp explains to the mayor of Rinde, and anyone else who will listen, just what genies are.

Going back to genies, there are four sorts, just as there are four Planes. Djinns are air creatures; marides are associated with the principle of water; afreet are Fire genies and d'ao, the genies of Earth—
Word has it old Monck had a way of forcing a djinn to serve him. There were rumours that he had more than one. He was said to keep them in bottles and make use of them when need arose. Three wishes from each genie, then it's free and escapes into its own dimension.
— pg(s). 250 – 251, The Last Wish (UK edition)

...once moved a mountain because it obstructed the view from his tower. Nobody has managed to do the like, before or since. Because Stammelford, so they say, had the services of a d'ao, an Earth genie.
— pg(s). 251, The Last Wish (UK edition)