ipad photo organization

The library is the place where Photos is storing all your photos.

You can build your own view of your photos on top of the basic library structure with folders and albums.

When you are using iCloud Photos, you can use the Shared iCloud Photos Library to split your library into two different compartments. Move the photos you have already organized in albums to the Shared Library and keep the photos that still need organising in your personal library. You can easily switch between the personal library, the shared library, or view both of them together.

Using the Shared iCloud Photos Library to have two separate libraries on all devices - Apple Community

This will work well, if you are already using iCloud Photos and do not need the Shared iCloud Photos Library for sharing your photos with others.

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.

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.

Nope.

Albums you create just contain pointers to the photos that exist in the Recents album.

You cannot move the photos out of the Recents album.

Are you asking about Photos on a Mac or on a Mobils device, like iPhone or iPad? Smart albums are only supported in Photos for Mac.