Things are very different in my case. Maybe because I did it all backwards, and first had the Gear S, THEN added the Gear 1? I can tell you that the app prompted me to update so the Gear 1 would work with it, and once "updated" is now all brown (you mentioned that yours never looked different). I think that's the doing of the Gear 1 software. I never had 2 Gear Mgr apps on the phine at the same time, the original one just changed completely. I can (from the now brown Gear manager app) switch back and forth between Gear S and Gear 1, but it messes with my Gear S battery.I'm probably preaching to the choir but have you tried uninstall the Gear app then install again? That's weird that the Gear 1 didn't work with it because I thought they had unified it to work from Gear 1 through S. A couple of Gear app updates ago I had 2 Gear apps on my phone after I updated it until I rebooted my phone then the old one disappeared. Same icon, same look when opened. I had a shortcut (not true shortcut but I don't know what you call it when you drop an app icon on your home screen) for the old one that also disappeared and I had to a new one back on. There were a ton of complaints about it and my last update was a few days after that. Mine has been fine since the last update .
I have not tried to uninstall and reinstall the app, because I think that would wipe my Gear S and 1, is that correct? If that is not the case, I may try to do that.
What I do now is basically connect my Gear S to my Note every few days to sync my running stats.
Not having the Gear S connected to my Note in any way shape of form gives me a much much better battery life than before. Gear Manager sucks the life out of the Gear S battery.