Use procedural textures from the Displace modifier in shaders
Some of the textures are already available in the shader editor, these include the Blend (Gradient in nodes), Magic, Musgrave, and Voronoi. However, when they are used in the Displace modifier they have different settings that are not available within the node graph, such as noise basis for some of the texture options.
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These are kind of two separate sections of blender at the moment. You have the "Texture menu," which has all the textures you use for the displacement modifier, and the shader texture nodes which are used in the shader editor.
Currently if you want a unified system, use the shader texture nodes with the "Real Displacement," option for rendering, as they are the ones that are most likely to be developed more in the future.
* @Zach Hixson * Thanks for explaining that they are currently separate sections.