If you have an Apple Music subscription, you can download content so that you can listen to it offline.
So the "remove download" option shows up when that song has been downloaded to your iOS device. Selecting it would delete it off of your iOS device but would keep it in your Apple Music library so that you could still stream it if you so desired.
The "Delete from Library" option would remove the song from your Apple Music library altogether and you would have to re-add it to your library if you wanted to stream it directly from your Apple Music library (versus streaming it from one of the numerous playlists that are available on Apple Music.)