Hi robert tfrombirmingham,
Thanks for posting. I understand wanting to make sure you're able to use the Music app as you expect, and I'd like to get a little information about what's happening to see how I can help out.
For clarification, are you saying these songs are downloaded to your device?
When you tap your music and see the "Browse" option, where are you tapping?
If the songs in question are downloading to your device and you didn't add them, are you sharing your Apple ID with anyone else? If so, this would be normal since the library is attached to your Apple ID.
While the specifics of what's happening would help to point to the best steps for this, it might be helpful to check your automatic download settings as a starting point. You can do this under Settings > iTunes & App Stores: Update apps or use automatic downloads
Have a good one.