Lighthouses, CoreLocation, BLE and "Geo-Fencing" - definitions of terms?

I was hoping someone could explain the relationship between iBeacon recognition, CoreLocation, and CoreBluetooth, specifically in the context of what iOS considers a "geographer".

First, I understand Apple's documentation on Using Regions to Monitor Border Crossings and have seen other discussions on the topic like iOS - CoreLocation and geofencing while the app is closed (especially pertinent to our app as it is a background operation). However, I'm having a hard time finding an explicit definition of Apple's geo object and exactly what structures are classified as such.

Consider:

• Beacons are based on BLE and yet they use the CoreLocation framework, not the CoreBluetooth framework. You don't actually need to add Bluetooth capabilities to your project settings to get them to work.

• Beacon region detection uses the same object and method calls: to register the region, you call the startMonitoringForRegion method of the CLLocationManager object.

• It looks like after we added beacon recognition to our application, users started seeing messages with "geo-fencing enabled" enabled in their settings.

I thought geo-fencing is exclusively used in GPS and Wifi based location services? Not BLE services? The whole point of BLE beacon signals is to reduce the battery leakage that geo-protection produces.

At a higher level, is there any way to prove that using beacon technology significantly reduces battery consumption than other location-based geo-fencing? Using "geo-fencing" as an umbrella term for both (if that's really what is happening) pollutes the waters heavily when creating a lighthouse business case.