1. Creating a new playlist on the web-based app will create said playlist on all synced devices.
2. Creating a new playlist on a synced device will not create said playlist anywhere else.
3. For playlists created on the web-based app (and thusly synced to devices), modifying (adding or removing songs) these playlists will sync the changes. If a song is added through the computer, it will be added to the same playlist on the device; if a song is added to the playlist on the device, the change will sync to the computer. The same is true of removing.
4. For playlists created on devices, changes (adding or removing songs) will not sync anywhere, for the reason stated in number 2.