Before cloning, I change the desktop picture via System Preferences > Desktop & Screen Saver. After the clone is finished, I change it back to my preferred picture. When booted from the clone, the desktop picture is therefore different.
I can't answer your question about the two desktop folders. Perhaps you could provide more details?
Jon
macOS 11.7.10, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365
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