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The following question was inspired by Effective pressure or what is the effect of presssure?, which may be accessed here: https://inside.mines.edu/UserFiles/File/CRA/2005/hoffman_etc_tle200612_effective_pressure.pdf.
My question is this: what exactly is pore pressure? Is it different from pore fluid pressure? An article or some type of visualization for an answer would be outstanding.
The concept of pore pressure is identical to the concept of pore fluid pressure, as you identified yourself.
The article rightfully identifies two pressure types: the confining pressure (those forces that try to compress the soil, like the weight of the overburden pushing on the soil) and the pore fluid pressure (the forces that resist compression; water, for example, is approximately an incompressible fluid, so it will resist the forces that try to squeeze it into a smaller shape. The pore fluid will thus be at hydrostatic pressure, but never more than that!).
Subtracting these two opposing forces gives what your article refers to as the differential stress. That formula, in words, is something like 'the possibility of the material to be packed tighter together, minus the resistance of fluid to being packed tighter together'.
This Wikipedia article can give some insight: https://en.wikipedia.org/wiki/Effective_stress , this video does some simple calculations: https://www.youtube.com/watch?v=chjEsWvLu5s . Does that answer your question?
