You can use Spotify with your phone over BlueTooth.
The in car streaming service is Slacker Radio. The Tesla subscription is equivalent to their Plus subscription. Upgrading to the Premium package gets you the ability to play music offline (on your phone, not on your Tesla) and the ability to play music On Demand. So, with a Premium account you get to listen to the song you request. With the account that comes with your car you may get the song you request, else you may get a different song by the same artist or a playlist seeded by the song you requested. The Premium is also your account, so you get to keep it as well as all your favourited songs and created playlists when you give up the car. You can also play them on your other devices capable of streaming music from Slacker.