Why can't photos be physically moved out of main folder into a new album?

Photos, (like iPhoto, Aperture, Music, iTunes) is a database. This means it can be very flexible and powerful, if sometimes a little confusing. The library is the core of the app. Every image is in the library. Albums are virtual, and are just subsets of the library. In fact, Albums are not places, they are lists - instructions to the app to 'display this group of images together'. So images do not get "moved" to Albums, they get added to that particular list. This means that an image can be in more than one album but use no extra disk space. Similarly in the Music app, all the tracks are in the Library and can be added to any number of playlists.

On a Mac:

If you're trying to organise your Library and want to find images not in albums, then a simple Smart Album

File -> New Smart Album

Album -> Is Not -> Any

will find these images. As you add them to albums they will disappear from the Smart Album.

On iPad or iPhone, which do not currently support Smart Albums, since iOS 18.3 identify images not in any album using a filter:

On the main screen tap on the up/arrow and select filter: Not in An Album. Further, you can check the bottom of the Info panel of a photograph for any albums that the image is currently added to.

The Library has intentionally been designed as the place where all your photos and videos are stored. Each item is only are stored once and the albums are referencing the photos there. This way we can use the same photo in many albums without having to duplicate it.

While viewing the library you can suppress the photos you have added to an album by using the filter. Set the filter to Not in any album “. this is possible in iOS 18 or later.

[ I'm just piling on, here. I figure OT will be along in a little while ]

If a picture disappears from the Library view when you put it in an album, then it's not there when you want to put it in another album. Thinking a picture can be in only one place really limits the versatility of an Image Manager like Photos.

As other have said, albums are just lists that 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.

If you have a recent version of iOS 18 on your phone, you can use the "Not in an Album" filter in the Library view to restrict what photos you see in the Photos and Library views. (If you are in the Photos view, drag down to the Library View.)

Double arrows icon -> Filter -> Not in an Album

Does that help?

[Sorry. That's on an iPad. My iPhone wasn't handy, but the principle is the same.]

Voxgendron wrote:

the photo you put in it still stays in the main library

That's the main idea. The main library is, erm, a library and custom albums reference it without taking any space.