How to effectively organize photos on iPhone without duplicates in the 'Recents' folder?

It would be helpful if you told us which iOS you are using. There is no Recents view on the newest system. You didn't tell us which model of iPhone you have, but if you can, you should upgrade to the most recent version. We can help.

In any case, you don't move pictures to albums. And you don't copy pictures to albums. If either of those were the case, then putting a picture in three albums, for instance, would take up three times the space.

In Photos, pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures from the Library that display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song,)  and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. You don't get fewer pictures in your Library because you remove one from an album; you just get fewer names in the album list.

So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon"  album with pictures of other people at the Grand Canyon. And it can also be in a the "September 2015" album with other things that happened then. Each album is pointing to a single file stored in the Photos Library, so having pictures in multiple albums takes up no more storage space. As you can imagine, this is very powerful in organizing pictures.

There are special views provided by Apple. How the Library View behaves depends on the iOS. In the newer versions, Library is provided by Apple to give a view of all of the pictures in the entire Library, and now, in newer systems, you can sort the Library in the order of their "taken" dates or their "added" dates depending on a your menu choice. You can also filter the Library and show only those pictures that are not in an album.

Your photo library contains all of your images. Those. images can be linked into any number of albums. These are not copies, just references. This allows you to place any image into multiple albums for custom organization. Recents is simply a view of the library that essentially contains all images in reverse order.

You can download any photo that you wish to your computer and sort elsewhere if you like.