hark you are correct. Just tested it and works like you said. I always thought that the image stabilization also stayed on when releasing the back button. Now that makes me think about using BBF. Have to give BBF a go and see if it works for me or that just using the shutter button works better for me..
Thanks all for the explanations. Have a great weekend.
Glad the info gave you a little insight. Here is a little something else to consider which sets BBF apart instead of using the shutter button for focusing. Since BBF uses AF-C, as long as the back button is pressed, the lens will continue to focus until you let go of the back button. Once you let go the AF stops. You can then press your shutter button to take the shot. This is helpful if you have a stationary subject and wish to recompose. So BBF is like using both AF-C and AF-S without having to actually switch between the two settings.
When you have a moving subject, keeping the back button pressed allows the lens to continually focus. If the area on which you are focusing isn't a high contrast area, the lens might have difficulty maintaining focus. And it's possible that is contributing to your lens hunting. That has more to do with a lens not being fast. You mentioned the lens being an f/4.0-5.6. When zoomed out to the tele end of its range, you will be at f/5.6. And depending upon the amount of light in the scene coupled with the contrast on the area you are focusing on, many lenses will struggle to maintain focus - not just that particular lens.
BUT when you aren't using BBF and are instead using the shutter button for both focusing and firing the shutter, if the body is set to AF-C, you lose the ability to focus and recompose. So there are advantages to BBF.
When using M, A, or S mode with my D7200, it is in AF-S with the shutter button doing everything. I have U2 programmed to be BBF, Manual Mode with Auto-ISO, and AF-C. So I can quickly switch between being in Aperture Priority with the shutter button to being in BBF with those setting simply by changing the Mode dial to U2.
At first it was a pain to switch back and forth because I wasn't too fond of BBF, but since wildlife tends to be my main subjects, I finally got used to it. And now I find myself still using BBF for landscapes and other subjects that I never would have considered.