How can I organize photos in albums without duplicating them on iPhone?

Odalisque wrote: Why can’t Photos be like Emails, where you create albums rather than folders and you can move a photo to an album and it isn’t also kept in a general library (inbox) so it is only in the chosen album(folder).

Both questions seem kind of the same, and I'm hoping that you want to know why Photos works this way rather than using the questions to complain, as some folks do. So I'm going to make as stab at this:

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. This is just like Music playlists-- you wouldn't want songs to disappear from your music Library just because you included them in a playlist.

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. Having a picture disappear from the Library would make it way harder to find it and include it in more albums. As you can imagine, this is very powerful in organizing pictures.

There are special views provided by Apple. The Library View is provided by Apple to give a view of all of the pictures in the entire Library in the order of their "taken" dates or their "added" dates depending on a your menu choice. Other views provided by Apple, like Trips or Favorites, are chosen by specific criteria, and that can't be changed.

Emails are defined by date, subject, sender. Photos are defined by who's in them (maybe lots,) date, camera type, location, objects in them, families, and many more things that we want to organize them by. So Photos offers a different way of thinking about pictures--as information rather than as things that can only be in one place or the other.

Maybe this helps to think like Photos thinks…

And to add to Richard Taylor's excellent explanation. Photos is consistent with the way other Libraries work on your device, such as Apple Music. The Library contains all the songs and you can add them to many different Playlists. It is not the actual song moved to the Playlist, it is just the link to the song in the Library. Just like with Photos, you can have the same song added to many Playlists and it does not increase the amount of Storage required because it is not the song being duplicated, and for the Photos app, you can have the same photo in many Albums without increasing the storage requirement.

Mail does not represent its data as a Library. If you delete an email from a folder, it is gone, whereas if you delete a photo from an Album or song from a Playlist, you still have it in your Library. You also cannot add the same email to a different Folder unless you duplicate that email and increase the storage required.

We are just other Apple users like you in this community forum. We cannot answer why Apple does what it does and Apple does not read these posts. But you can offer your feedback to Apple directly here:

Product Feedback - Apple