Yea the apple battery cases really do act like an extended battery for the phone. They report their charge level in iOS as well. The charging and discharging is automatically managed instead of having to turn on the charging like on third party cases. The problem with waiting until your internal battery draining before switching on the external battery is that it uses up a charge cycle on the internal battery. If you can keep the internal battery close to full for longer then you can extended its useful service life.
Another smart feature is that the Apple battery cases don't trigger the "I'm plugged into a wall" power profiles in iOS. This means that even though the smart battery case is charging the phone it won't trigger actions like iCloud backup, photo uploads, photo analysis, etc... which drain your battery like crazy.
Aftermarket battery cases like Mophie or other cheap ones just act like a battery bank or a normal wall charger. The phone has no idea its running off a second battery. So it will behave like you are at home plugged into the wall.
You also won't find fully functional lightning ports on third party battery cases. The ones that have lightning ports will only charge. No data or audio pass through. The apple battery cases always behaved like the native lightning port on the phone.
