Also plenty of people don't realize/know/care that youtube is owned by Google. They are still a pretty independent brand from a consumer perspective.
"And as a special bonus - YouTube Red works with Google Play Music, so subscribe to one and automatically get access to the other."
http://youtube-global.blogspot.com/2015/10/red.html
So, they're different, but as each includes the other and they have the same $9.99 price, the difference is essentially purely academic.
Also plenty of people don't realize/know/care that youtube is owned by Google. They are still a pretty independent brand from a consumer perspective.