Waste, desert, badlands, wilderness can mean a tract or region of land not usable for cultivation or general habitation.
Waste is the general term applicable to a tract or region which because of natural features (as poor stony soil, excessive wetness or dryness, or abrupt elevations) or because of barrenness induced by human agency is unfit or unsuitable for cultivation or human habitation.
Desert tends to stress aridity; it calls to mind arid regions where areas of shifting sand prevail and there is little or no vegetation, but technical use generally applies it to regions that have less than ten inches of annual rainfall or are incapable of supporting a significant population without an artificial water supply.
Badlands applies to a barren waste where soft rocks that suffer from continual erosion prevail and hills are steep, furrowed, and often fantastic in form, drainage is labyrinthine, and watercourses are normally dry.
Wilderness may apply to a waste which human beings find not only incapable of cultivation or habitation but difficult to make their way through for lack of actual or even possible paths or trails, but perhaps more often the term denotes an area or region that has not been extensively occupied or cultivated by man without implying anything about its potential uses.