Bluetooth on Ubuntu Core is provided by the BlueZ stack which is an official Linux Bluetooth protocol stack. The lower-level part of it comes with the kernel snap while the user-space portion can be installed as a separate snap.
The Bluetooth interfaces on Ubuntu Core
On Ubuntu Core there are two interfaces which define the communication of the Bluetooth stack:
You can learn more on the interfaces documentation.
Note that unlike the bluetooth-control interface the bluez interface is not installed by the core snap, neither the gadget nor kernel . It shall be installed by the application snap.
Putting it all together
As you know now there are two Bluetooth related interfaces on Ubuntu Core, the: bluetooth-control and bluez . One of them is provided by the core snap while the another is provided by the application snap.
On a system without bluez snap installed, type:
$ snap interfaces | grep blue :bluetooth-control -
Observe that there is a bluetooth-control slot provided by the core snap. This is unlike to bluez because no snap exists which provides a slot based on the bluez interface. You need an application snap to reveal it.