When you moved them, they probably got re-indexed, causing you to lose customization. You'll have to rebuild the playlists, if for no other reason than the song address (internal vs sd) has changed and it didn't update automatically.

 

As it's a new Samsung micro-SD, where did you buy it, e.g. cheap online from Ebay? Music not playing, data changing and corrupting unexpectedly, etc. you may want to check it with SD Insight.
https://play.google.com/store/apps/details?id=com.humanlogic.sdi
If the Samsung micro-SD does turn out to be a counterfeit, hopefully you'll still got a backup copy of your music library somewhere.

 

OK, definitely check it then with SD Insight. If the manufacturer comes up as "unknown" or "invalid" rather than "Samsung", it's almost certainly a fake micro-SD. AFAIK third-party vendors on Amazon can be as notorious as Ebay for selling knock-offs, no matter how good their feedback appears to be.

What you're describing is very much the symptoms of a counterfeit micro-SD, and both Samsung and Sandisk are the most often faked.

 

If you get your issue solved and chose to do this again. Its safer to use a PC or Laptop to transfer files on your device from one place to another.