So we're both on the same page let me restate the issue:
1 - both albums are albums in the Photos library, correct?
2 - how are you deleting the photos from the first album? If you use just the Delete key it will delete it from the album but not from the library and thus the other album.
FWIW albums and photos added to them do not take up additional space on the hard drive. They are just pointers to the original photos. If you're familiar with iTunes albums are to Photos as Playlists are to iTunes.
So if you've deleted photos from the library you can go to the Recently Deleted album and recover them within 30 days.
The following describes how deletions are done in the library:
Deleting Photos from a Photos Library
1 - regardless of where you are in the library, i.e. Moments, Collections, albums, smart albums or projects, 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.
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.
