[Help] Volumetric shadows geometry shader in HLSL

Hi
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.