When you're looking at Library or Recents, those aren't really albums-- they are preset views provided by Apple. Recents view shows all the pictures in the entire Library in the order they were added. You can't remove a picture from the Recents View, because that would be deleting it entirely. 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. The . The Hidden View shows all the pictures from the entire Library that you have marked to be hidden. You can't change how these views work. These albums always provide the same view so that, when something goes wrong or seems off, you (and we) can depend on them always showing the same thing, and there's no chance that someone snuck in and changed the order or removed pictures.
And keep in mind that, 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 to 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. You don't get fewer pictures in your Library because you remove one from an album; you just get fewer names in the album list.
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. As you can imagine, this is very powerful in organizing pictures.
By the way, Recently Deleted is also just a special view of all the pictures in your Library that you’ve marked to be erased. The names of those pictures are still on the album lists; they’re just not shown. If you “restore” a picture from Recently Deleted, then they are shown again in all the albums that had listed them. Hidden is similar— the names are still in the album lists, so when you un-hide a picture it shows up again in all the albums it had been in previously.
This is a lot of info-- I hope it helps....
