If you want to save the content of the Playlist tab you can do it: Playlist tab > Add to Saved Playlist (it let you add or create a new 'Saved Playlist').
Then you can access that playlist in the Library tab under the 'Saved Playlists' folder.
As explained by SimBun you can also export/import all the 'Saved Playlist' to a file archive.
Additionally you can export a 'Saved Playlist' to m3u or xspf file formats using 3 dot menu on 'Saved Playlist' (in the 'Saved Playlists' folder)
and actions 'Export to M3U8' and 'Export to XSPF'. Though these export actions are more for interoperability with other apps or programs.