Sync makes your DMS and your PMM library look the same. It does this by look at the timestamp for the last modification to a file. If you erase a file from your PC, but it's still on your DMS - when you sync, it will be removed from your DMS. When you add songs to your PMM library and "sync," they will be added to your DMS.
I have never used the sync function so I can't vouch for whether or not it's any good. I know when we were beta testing it, it sucked.
Refresh database is what you use if you think you have music files on the DMS that are not showing up in the database (ie: you can't get to the songs when you're in the car.) It scans the DMS for all music files and makes sure that they're in the database.
I hope that helps and that someone will correct me if any of that is wrong.