When you browse your music library you will see all the songs available from iCloud. If you have changed the iTunes Match configuration in the system settings to only show files which have been downloaded, then only downloaded songs will be shown.
Note – You may see an “Unsupported File Type” message if the song has not been downloaded to your device. Go into the Music app on your device and ensure the song is downloaded before attempting to open it with Anytune. Unfortunately, Apple does not provide a means for Anytune to download the song automatically on your behalf.
Anytune can play files in your device’s music library. Anytune will automatically show you songs that have been sync’d from iTunes to your device (downloaded to your music device’s library). You can also see songs that are available for download but not yet in our Library.
These will show as greyed out and when you tap to play this song you will a message:
iTunes Match: “This song has not been downloaded yet. Please go into the Music app and download this song.”
Anytune has a Setting > Show All iTunes Music that allows you to hide songs that are not physically downloaded to your device.