Local (downloaded) music on iPhone On iTunes I set up a smart playlist to contain only downloaded music (iTunes Match) so that I can use it offline or when the connection has a very low quality (see for example Create a Smart Playlist for iCloud Songs that have been downloaded Locally)

I would like to achieve something similar on my iPhone.

I know that I can create a smart list on iTunes but the logic will refer to iTunes and not the iPhone. For example my "downloaded music" list is also present on iPhone but the songs are the one downloaded in iTunes not iPhone.

Did I miss something? Is there a way to create a similar list or to listen to local music only?
Did you turn off iTunes match on your iphone?Maybe you should try to turn that off and you might need to also toggle the music player setting to local files only: go to Settings > Music and set the option for "Show all music" to OFF.