They are not the same. YouTube Premium offers you wide range of benefits, which includes YouTube Music, YouTube Originals, Ad-free viewing experience, Background play. Thanks.
YouTube Music is different from Google Play Music, as it has YouTube’s catalog of remixes, live, covers and music videos in additional to official songs. Here's more info about benefits of YouTube Music and YouTube premium: https://goo.gl/4Ky74u . Hope this helps.
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