The least destructive approach I've found is to:
On an iOS device, force- or long-press on the song in question in the Music app, and select Delete from Library.
On the Mac, wait for the iCloud Status to change to Removed.
On the Mac, right click the track and choose Add to iCloud Music Library.
Doing it this way ensures that the song is never removed from ...
To simplify when using iTunes Match, your phone or other device, connected to the internet, can play "your" music from Apple's Servers. Apple scans your physical music Library and then "Matches" the songs to songs they already have.
This means that if Apple has a song on their server that "Matches" a song in your physical Hard Drive music library then it ...