Register in place will keep all the files required for that VM right where they are (on a NAS or USB drive for example) and Hyper-V will run the VM from that existing location. The unique ID is like the Hardware ID for a physical computer. This is what the activation for Windows is tied to. Use the existing unique ID and Windows stays activated. Create a new unique ID and Windows will deactivate and require a new activation.
Restore the virtual machine copies all of the files for the VM to your Hyper-V default location but does not create a unique ID.
Copy the virtual machine copies all of the files for the VM to your Hyper-V default location, but it does create a new and unique ID for it, making it basically a new machine.