The following interpretation is based on much experimenting. Getting to this distillation, it has been as vital to read widely, including Steve's magnus opus...
Each AF mode functions at the intersection of 3 variables:
1. Coverage of subject
2. Front-Focus Priority (tendency to ignore background objects)
3. Dynamic Coverage
These are constrained to a delimited domain with out boundaries prescribed by the AF sensor in a DSLR / AF pixel layout in the MILC sensor. Not all of available do #3. #1 is basically irrelevant for Single-Point in AFC (even tighter so in AFS Pinpoint) and moves around on manual (by thumb).
There is the increasing complexity injected by pattern recognition - Face and Eye recognition. The new D6 AF algorithm incorporates human face recognition into some of its AF modes.
'Out There' one seeks to focus on a specific subject, and often a precise part of the subject - often the eye(s). This is why many of us use Single-Point most of the time.
> Dynamic Area modes [a9, a25, a73 etc] expand the effective coverage of Single-Point (bit like a net to my mind). Obviously, widening the area incrementally.
> Group Area mode appears to maximize Front-Focus Priority (in most Nikon cameras but the Z7 IME lost this plot, although somewhat improved with firmware). This mode also still works at slower lens speeds > f5.6
> 3-D Mode seems to work effectively against neutral background and with sports action (implying designed for humans primarily).
> Auto-AF works well in minimal background and/or dominant subject. Only invoked for moving subjects. Auto lacks precision, as it tends to grab the most obvious surface of the subject (tends to miss the eye). This mode is not an option at lens speeds slower than f5.6.
In practice, using Df, D780, D7200, D500, D850 I have used single-point for most subjects, and over the past~3+ years with D500 and D859, my 2nd most common mode is probably a9 or a27 for wildlife: Group or Auto for active subjects. Auto is sometimes better for flying birds with no interfering clutter. In summary, choice of mode aims to maximize precision and accuracy for the subject, and particularly its motion (still, moving, erratic).
The above is biased to Nikon only.
One other variable - constraint rather - is the area of AF sensor points, and their coverage. This varies with lens speeds/cameras. The main thresholds are f4 and f5.6, and check Nikon's tech data as to which lenses.