It really is critical to understand these terms and the differences between these things.
Folders are the real folders on your computer's hard disk:
Picasa is working directly with the folders and photos on your computer's disk, so folders aren't anything Picasa invented or creates. It just reads/uses them from your computer just like other applications on your computer; example, Windows File Explorer, Lightroom, etc.
Folders actually contain the real photo files (example, jpg files)
When you delete a photo from a folder in Picasa, you're really deleting the real photo from the real folder.
The photo will also be deleted for all other applications including Windows File Explorer
When you move a photo from one folder to another in Picasa, you're really moving the real photo between real folders. They will also be moved for all other applications, such as Windows File Explorer.
Folders on your computer have "Manila Folder" icons.
Albums have "blue book" icons.
Albums do not actually contain photo files. Albums don't have their own copies of photos.
Albums "reference photos" or "point to photos" or "present photos"; therefore, albums take negligible disk space.
You are never "moving" a photo from a folder to an album:
When you put a photo in an album, you are simply telling Picasa to make that album include a reference to that photo.
When you delete a photo from an album, you are not deleting the real photo from the real folder. You are simply telling Picasa that that photo should no longer appear in that album.
When you delete a photo from an album, the photo remains in its folder and in any albums that may reference it.
A photo can appear in multiple albums, but it still only exists once on the computer (in its folder).
At this point, it should be clear that you should not delete the photos in your folders and expect albums to survive. If you delete a photo from a folder, it is really deleted from the folder, and from any albums that may have referenced that photo. Without the photos in the folders, albums have no photos to reference.
If you're using Albums in Picasa, do not move photos around using Windows Explorer or some other tool or program. This can badly confuse Picasa, and your albums will likely lose sight of the photos they were referencing.
If you're using Picasa, use Picasa as your photo organizer. If you move the photos using Picasa, Picasa will always update any albums that reference the photos so that they know about the new photo locations.
In Picasa, you can move photos to a existing folder:
By dragging thumbnails from the right side of the Library view to the folder in Picasa's Folder List on the left of the screen.
You can select some photos in a folder and right-click on them and do a "Move to new folder..." on them.
And you can move an entire folder to a new place (even a new drive letter) by doing a right-click -> "Move Folder..." on a folder in Picasa's "folder list."
Move photos around this way and your album definitions will be fine.
Albums are a GREAT organizational tool. They let you add multiple ways to view your photos without having any photo-duplication on disk.