YouTube Music Premium is included in YouTube Premium but can also be purchased as a standalone product for $9.99 a month.
It includes music playlists, music videos, remixes and live versions of songs. Subscribers of Google’s Spotify competitor, Google Play Music, get this as part of that subscription. Google Play Music costs $9.99 a month, so your best bet is to just subscribe to that and then you get YouTube Music Premium included.
Again, unless you’re focused purely on music, you might as well pay the extra $2 a month to get YouTube Premium.