Music on device that isn't in iTunes

I just bought a new iPhone 8 Plus running iOS 12. I previously had an iPhone 6 running on iOS 11, and when I set up the 8, I restored the phone from the backup of my 6. I had this problem on the 6 and now it has seemed to carry to the 8. When I open iTunes, it shows 'no items' on my device. When I open my phone and go to the Music app, there's tons of artists and songs, all things I have purchased with iTunes, with the cloud icon next to them. To be clear: I NEVER purchase music on my device, always through iTunes on my PC. Again, NONE of this music was purchased from my actual device. When I listen to music on random, in my car for instance, not only will it try to play some of these songs that are not in iTunes 'on my device' but not even on my phone if I search for them. If I try to delete any of these items from my phone, it tells me it will be deleted from all my devices. I don't want to do this as some of the music is on other devices that I want to keep. In iTunes, the only option I have checked on the summary screen is 'manually manage' and on my phone, in iTunes and App Stores, I have all automatic downloads off. What can I do to fix this, it's so annoying.