Hi Phloptik,
The three areas are called “Umbra”, “Penumbra” and “Antumbra”, and are in used since (?) ever, for example to describe in paintings the way a shadow is created.
It is based on a relationship to the size of the light source, the distance, and the objects (casting and receiving).
The Penumbra is the partially created shadow, partially, at least to my understanding, based on the limited used area of the light source itself, e.g., the sun. In other words the constellation between light source and the size of each in relation.
If you like to adjust the shadow in that way on the object itself, use the simulation (fake!—but fast) of the Detail>Contrast. If you like to have these qualities on objects that receive these qualities (and with that as well on the casting and self-shading object as well) you need to use area lights as well as shadows.
BTW: “Soft-Shadow” (C4D-term) is a simulation-method, and based on an exploration of the space, like something along raster-points and there the interpolation of such. If you like a good quality, avoid “Soft-Shadows” (as the name of the shadow option is use in C4D more or less wrongly) all together.
The way the light is calculated on an object is certainly dependent on the Illumination method as well (such as Blinn or Oren-Nayer). It all plays together, and is on the end based on formulas, rather than reality. In GI you might not see the effect of the Illumination settings mentioned, while using only objects (with luminance) and images to illuminate a scene.
The “Gradient” might look partly in that way, but is not the same, if the word Penumbra is used as in science or art.
The Fresnel is a lens that takes advantage of the fact that the change of medium and the angle where it happens is more important. In that way the Fresnel Lens is a lens which is step by step reduced in depth, and roughly creating the same effect as a full lens. In that way it is lighter in weight, stores less heat and is over all easier to handle.
Good luck with set up, sounds like you take care of details :o)
All the best
Sassi