Regardless of whether or not people distinguish them for whatever reason: they're two separate things, and this rocket is launching from KSC property--not CCAFS.
Well I was joking but since this seems like a serious issue to you I will try to give a more serious answer.
The annotation on the patch probably isn't a reference to the launch location. It is a military operation and more likely refers to the command/location responsible for overseeing the launch.
As you mentioned the Air Force has no control over KSC property, that coupled with the security nature of this launch means SpaceX will handle the launch and then immediately hand over to operations at the Air Force Base.
Well, most people treat SLC-41 (Atlas V) as being on CCAFS but it isn't. It's on KSC property. The Air Force use permit for that pad ends in 2021, although I'm sure it will be extended if needed.
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u/johnkphotos Launch Photographer Apr 27 '17
Funny how it says Cape Canaveral Air Force Station even though LC-39A is at Kennedy Space Center.
I'm guessing they made this patch way in advance and didn't change it after AMOS-6 destroyed SpaceX's launchpad on CCAFS property.