It is difficult to know what you are referring to with your question since different teachers use different approaches and different analogies...
For example, I have never heard of the screwdriver analogy, so I could only speculate as to how that analogy would correspond to my personal understanding, which may be different that what your teacher is trying to convey.
While I use the image of a circle when I teach, my approach is that the circle is merely one plane through a sphere, and I tend to emphasize the sphere more. Perhaps if you expand the circle that you are currently thinking of into a sphere (both circle and sphere with the same center), then it may better ‘link’ your circles together?
Another possibility is to think of your circle (or sphere) more like the following diagram:
Here there are actually an infinite number of circles (or spheres) with the contact point common to all of them (near the bottom of the above image) being the point of contact with your partner/opponent (the point of application for form). Therefore, you can switch from one diameter circle/sphere to another instantly without a change in the point of contact (changing the center by changing the diameter of the circle/sphere).
If the above is not addressing your question, then please clarify what it is that you wish to know.