Typically, Windows picture apps don't require the pictures to be in a specific folder to be able to be viewed. What is the "different program" that you are using?
Many picture viewers create a database of your pictures. The database "points" to the physical location of the pictures on your drive but don't actually move the files to a different folder. As gigagiggles said, these type of programs have an import function that scans folders/drives to locate the pictures on your system to build the database.
In regards to the pictures that aren't shown when you look in "My Pictures", what are the filetypes for those pictures? It may be possible that those pictures are of a type that isn't recognized as a picture format. "My Pictures" is setup to only show picture files, to see all the files in that folder, you need to right-click on the folder and select Properties, then Customize. On the Customize dialog there is a dropdown box that is labeled "Optimize this folder for:". That dropdown is set to Pictures by default but you can change it to General Items to see everything in the folder.