The mobile key is a key just like the key fob is, it is separate from the Lucid app. Both the mobile key on you phone and your key fob use a publics and private key to securely communicate with the car. You do set up and create the mobile from within the app, but the mobile key is much different than the app. If you look a Bluetooth devices on you phone, you will see two. One for the typical phone to car Bluetooth connection and a second for the mobile key.
Mobile key is the terminology used by Lucid so it makes sense for us to use that same terminology here.