I have lots of songs already on Apple Music, now I want to switch playllist from Apple Music to iPod nano. I choose converting Apple Music songs to MP3 or FLAC at first, after getting the Apple Music songs as local files, and then sync the songs to my iPod nano by using iTunes.

I have ever use this Apple Music Converter to convert Apple Music to MP3, FLAC, M4A, AAC, after downloading and convert Apple Music songs to MP3, I can easily transfer Apple Music playlist to Spotify App.
I use a third party iPhone transfer tool to sync the songs from iTunes to iPod nano. In addition, you can also transfer Apple Music to your Android devices, MP3 player for playing offline.