When I move photos to a folder, they still show up in Photos. How can I change that so that they only stay in Folders?

Photos, albums, smart albums, memories, projects are all just different views of the same original, master image file. One can have an image in multiple albums, projects, etc. and not take up additional space on the hard drive.

If you're familiar with how iTunes handles playlists then albums are the playlists of Photos.

You would need to delete the photos from your Photos library after first having done a File/Export of the Photos to your Mac. Do a File/jExport rather than dragging the thumbnail out of Photos so that you carry the photo's Metadata (title, keywords, description, location info, etc.) with it if you want that. You need to check the appropriate boxes in the export box. The Metadata will appear in a sidecar file along with each photo. If you keep them together you will preserve the Metadata.

In the Photos app you are only working with thumbnails. The originals remain in a master folder and they are never changed no matter what editing that you do to the thumbnails. You must never mess with the master folder. However, if you delete the photo thumbnail from the Photos library, you also delete the original.

-- Rich