When you use the "Move" function of Motion Explorer, all of your files are transferred from one storage drive to another. The original files are transferred to the destination and no longer reside in their original location. The description in Motion Explorer is updated with the drive letter and path of the new location.
When you use the "Export" function of Motion Explorer, all of your files are bundled into an "Export" file and an associated folder. You have the choice of deleting the raw data on the original computer or keeping both copies, the original and the exported version. If you choose to Keep the raw data, the Location shown in Motion Explorer will be the original path, not the exported path. If you choose to Delete the raw data, the entire file(s) will be deleted from the computer and inside of Motion Explorer. When you "Import" a previous export, the data will be placed back in the original Hierarchy as defined at the time of the Export.