You know how you can watch Netflix on your TV, and another person can watch on another TV, or an iPad? Well, you can’t do any such thing with Apple Music. As Apple says in their documentation:
Note: You can play Apple Music and Radio tracks on only one device at a time unless you have an Apple Music Family Membership, which lets you play music on multiple devices.
In a way, this is fair, but you need to be aware that if you leave music playing on one device, and want to play on another, the first one will stop. Here’s an iTunes dialog when this happens:
I was listening to music on my Mac, and started playback on my iPhone, which paused the music in iTunes.
Not surprising, but something to be aware of.