Hi @Anonymous
Half of your question is explained in this section of the help: Distinguish Coincident Constraints. This explains the white dot and the "no dot" displays, but does not explain the black dots (or, more accurately, this type of black dot display - black is also used for spline fit points).
In your case, the black dot indicates a "point stack", meaning that there are multiple points on top of each other. This is common with circles, which do not share points, like line endpoints do. I will send a note to the documentation team that the help is out of date here...
You can also see this using Select Other. If you press and hold the left mouse button for 1/2 second or so, it will bring up a dialog that shows you everything underneath the cursor. In the picture below, you can see that there are actually 3 points at this location. If you move the cursor over each entry, it will highlight the curve that this point belongs to:

In this case the first point in the list is the center point of the inner circle.
Hope this helps,
Jeff
Jeff Strater
Engineering Director