Volumetric shadows geometry shader in HLSL

For an upcoming schoolproject I want to create a geometry shader that creates volumetric shadows. I’ve spend the afternoon doing some research but I got quite confused with some things.
I see all different names surrouding the topic but I am curious if they all mean the same like ‘Geometry Extrusion with geometry Shader’ or ‘stencil volume shadows’?
If anyone could point me in the right direction on where to start with this shader I would greatly appreciated it.

Volumetric can’t be geometry shader, geometry shader draws geometry. Volumetric shadow is a raymarching technique done purely in the pixel shader using distance function evaluation (raymarching) you can see a lot examples on shadertoy.
Technically speaking you can try to create some sort of shadow projection with geometry shader, stencil in this case will be a sort of flag on your depth buffer that you can extract only this drawed geometry from depthbuffer.

check out this volumetric spot light.
This is a ray marching approach - so no geomery shader involved, but done in a pixel shader as antokhio pointed out.
There is also a link to the source code and an article giving a short explaination of this approach.

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