How to use a back-up drive to also carry files between two systems?

I use a portable WD MyPassport to back-up my Windows 8 laptop.

I would like to carry 200GB of data from my old Windows Vista Desktop over the laptop through this WD portable harddrive. When connecting it to the Windows Vista Desktop it recognizes the drive and confirms the WD Unlock. But the drive doesn’t allow space for recording the files, indicating that there is no file space available (though the harddrive has some 800GB free space).

What do I do wrong? How can I copy files from the Windows Vista Desktop onto this portable backup drive?  

Hi latuman, how are you trying to copy your files, manually or using a backup software? You can check the following links for information on how to do both.

How to move or copy files from one hard drive to another in Windows

How to create a category backup using WD SmartWare