For displacement, you have many options, such as marble, clouds, etc., but the node editor only has musgrave, voronoi, and noise. Why is this? Is there a way to obtain these noise options in the node editor? Any answers are appreciated :)
The textures you find in the node editor are render engine based shader nodes, what you see is dependent on currently active render engine, and only available at render time, and in some cases to the basic OpenGL viewport preview.
On the other hand, textures available for Displacement (or any other modifiers for that matter, like particles, hair, painting among others) must be available at all times, even before rendering, and regardless of the currently active render engine, such as third party ones.
For the purpose of this answer I'll assume you are using Cycles as active render engine, and by the "node editor textures" you mean Cycles Shader nodes.
As such the textures you find in the node editor are Cycles Shader textures, capable of GPU computing and other Cycles exclusive features. They only really work if Cycles is used as render engine, and are generally computed at render time, making them unavailable for use in modifiers.
For modifiers, Blender Render based textures are used instead since these have been around far before the emergence of Cycles. They supporting a different set of features and aren't bound by the same constraints required by Cycles. These are computed in different ways, on CPU only, and rely on Blender Internal, and as such are is available at all times even if Cycles isn't being used.
You can't really use Cycles shader nodes for modifiers, and the opposite is also true, you can't use Blender Internal textures for Cycles shader trees.
For future Blender 2.8# version there are plans to retire the old Blender Render based textures and replace them by a modern Cycles compatible node system, but it will not be available any time soon