How can I store photos on my desktop without iCloud?

If you have icloud photos enabled and sync using the photos app, anything in photos will sync. You would need to remove the image from photos to stores elsewhere.

If you have desktop and documents set to sync, then files added to those locations will also sync. You would need to move the photo elsewhere.

I'm not sure what you mean by "move photos to desktop." In Finder we use Drag & Drop to "move" files, but that's more confusing with pictures. Photos can generate lots of versions of a picture-- versions that are edited, or thumbnails, cropped, or previews, or original files, for instance. If you drag & drop, you only get one of the possible versions, and it's hard to predict which.

If you want to "move" the original, unedited, uncropped, uncommented picture file, then you should use the menu choice "File>Export>Export Original." If you want to "move" your latest edit with comments, then you should use Flle>Export>Export nn Photos," but you will need to decide on the size and quality of the image you want. You may want to "move" both the original and the edited versions.

You can constantly turn it on off. Or, just leave it on and move your photos. Once moved, you would delete them from Photos to remove those images.