It seems to me that you are thinking of a picture as a thing that can only be on one place.
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. And you probably don't expect a song to be removed from your music library because you put it in a playlist. It just doesn't make sense.
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. This is only possible because of the way Photos makes use of lists of pictures from the main Library. As you can imagine, this is very powerful in organizing pictures.
There are special views provided by Apple. 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. You can't remove a picture from the Library View, because that would be deleting it entirely. The Recents view shows all the pictures in the entire Library in the order they were added. 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.
On a Mac, by the way, we have Smart Albums. We can set up a Smart Album to show only pictures not in an album, for instance. What Photos for iOS really lacks are Smart Albums.
So think of albums as playlists. Does this make sense of what's going on?
