Why do the Picts stay in both places after you put them into albums?

Albums are not storing any photos. The photos are only stored once in the Photos Library, independent of the number of albums you are adding the photos to. The albums are just an index to group the photos and are referencing the on copy in the library. If you delete the photo from the library (from Recents, All Photos, or any other view created automatically by photos), the photo will be removed everywhere, from all albums you added it to. You can remove photos any album you create yourself, because that will just remove the reference to the phot in the library, but deleting from the library views will remove it everywhere.

If you need away to see, if a photo has been added already to an album, you may want to tag the photos in the albums with the favourite heart. Then you can see directly , if a photo has been added to an album. I am only adding favourites to my albums anyway.

Or duplicate the All Photos album as an album of you own "My all Photos". From your own album you can remove photos after you add them to other albums.