Well - the way it is supposed to work is the songs/albums/playlists you select as "make available for offline" are supposed to download to your iPhone or other device. This download process seems - at least in my experience - very hit or miss. Smaller playlists - like the ones suggested in For You - seem to have less problems than larger ones or ones you create yourself. (Though the smallest ones I have self created are around 100 songs and they are selected randomly as a Smart Playlist so perhaps that is the problem.) Sometimes all the songs will be downloaded, sometimes I will get various error messages - usually the "Looks like this is not available anymore" which seems strange as most of the songs are my own songs, sometimes I will get 97, 98 out of the 100 songs (like the playlist I did today).
But they are stored in your iPhone until you again tap those three dots and tap remove downloads. Then they will be removed from your iPhone's memory. You can also go into Settings/General/Usage and delete the music from there, not sure what effect if any that will have on the way the Music app displays what is available or not.
