The Recents, albums, smart albums, Library, Favorites, Places, etc. are just like playlists in iTunes. A photo can be in many albums but there is only one file in the library - just like a song file in iTunes.
Each of those items are just pointers to the original file in the Library view. See below for how to delete from the various items/views:
Deleting Photos from a Photos Library
1 - regardless of where you are in the library, i.e. Photos, Memories, Favorites, People, Recents, Imports, albums or smart albums, select the photo(s) you want to delete and use the key combination of Command+Delete to move the photos to the Recently Deleted smart album. Without the Command key held down you'll be presented with a confirmation Yes/No window regarding the deletion.
2 - click on the Recently Deleted smart albums in the sidebar.
NOTE 1: If you're using Photos 1.2 or earlier use the File ➙ Show Recently Deleted menu option.
3 - in the Recently Deleted album you can opt to let the photo automatically delete after the 30 day waiting period is up, delete them immediately or restore them to the library.
NOTE 2: deleting a photo from an album, slideshow, book, etc., with the Delete key only deletes the photo from that item. There is no key combination that will delete a photo from a project and move it directly to the Recently Deleted smart album.
NOTE 3: deleting a photo from a Moment or Collection (the Photos window) or the All Photos window deletes ALL occurences of that photo in the library.
If you delete out of the Recents album to the Recently Deleted album and then complete the deletion from there all occurences of the photo will be deleted from the library.