iPhone remote apps - “Apple TV Remote” vs ... something else?

Solution 1:

They are different "apps". The one in Control Center is not even a full-fledged app. You can't switch to it, or close it, like regular apps. I think I end up using the one from the Control Center more, since it's easy to launch, and I think that's the one that integrates better with Apple Watch (I can use my watch to control the ATV, if I start the remote on my phone first).

Notice the multiple uses of the word "think". This is not an obvious design choice by Apple. The Control Center icon should just call a single full app, just like if you click on the Camera, Alarm, etc, in the Control Center.