Re-check your Samsung manual in regards to how to use. I am not referring to the Drive Manager manual.

Make sure you are choosing the correct Desktop icon. ie: the external drive and not the Samsung Drive Manager.

One thought is to open your user Desktop folder and arrange view option so you might see if you can open via clicking any folder icon or arrows.
Another method would be to go to the My Computer/This PC system folder/window that shows connected drives (Devices & connected Drives); such as drive A, C, D, etc.

The following image below is not the best of examples but same concept.


I do not have any external drive that opens via a drop-down menu! (though you did not specify whether it's a menu bar or right-click menu.)
I suspect you are attempting to open the Drive Manager utilities.

It is often a good idea to rename your external drive so it is immediately recognisable and cannot be confused with any other device or folder. Perhaps not using Samsung in the drive's title, in that way you will not confuse the Samsung drive manager or utilities with the actual drive.