Re: What I would like to know.
Yes, you can only play Google Play Music content on Google Play Music.
However, at least Google make Play Music, Play Movies and TV, and Play Books available on iOS.
Compare and contrast to Apple apps on Android.
Now I'm sure someone will pipe up and say that Apple Music is going to be available on Android, and this is true, but let's not kid ourselves that this is some sea-change from Apple. The *only* reason they are supporting Android is family sharing - they know damn well that they have to support cross platform family sharing if rivals like Spotify are able to do this, because not every family is all iOS or all Android (in my case, my wife uses iOS devices, but I prefer Android).
I wouldn't be at all surprised of Apple Music for Android only works with a family subscription when it is eventually released.