keeping photos in album but not in library

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:

Check out HashPhotos

https://apps.apple.com/ie/app/hashphotos/id685784609

It integrates with Photos on your iOS device and adds a Smart Album feature. Using this app a search

!#inalbum

Will find images not in an album

(Hat tip to User ukSamo for the recommending this app.)

There is no option to do that. The Library contains all photos whether or not they are displayed in an Album. Note that there is only one photo stored and it is displayed in multiple places.