[Contains potential spoilers]
As leader of the Minutemen, I already had control of a dozen settlements or so before I joined the Brotherhood of Steel.
I started a radiant quest for the Proctor to requisition supplies from one of my settlements.
When I went to my [Minuteman-controlled] settlement, I spoke to the indicated settler, and passed an easy persuade check to convince him to donate food to the BoS. (I also saved beforehand, and tried other methods, such as paying for food, with same results).
As soon as I made the deal, I received a notification:
The Brotherhood now controls this location.
Question: What are all the differences between Minutemen versus BoS being in control of a location?
I googled around and did not find a definitive answer - just lots of speculation and confusion on Reddit and Steam forums. Some folks complain they cannot built/modify the settlement at this point, but I had zero problems giving orders or building/moving turrets/walls/furniture/whatever; however, I did not try this after returning to the Proctor, only immediately after making the deal.
I checked map on my pip-boy, and still see the supply lines and it appears that I still "own" the settlement. Since it's just a radiant quest I reloaded my game until I understand exactly what I'm getting into.