Photos

If you have iCloud Photos checked in your Photos Preferences, then yes, deleting a picture in one Library deletes it in all linked Libraries.

But deleting a photo from an Album doesn't erase the picture-- it stays in the Library and is just removed from the album.

Using Command-Delete removes the picture from the Library and all the Libraries synced through iCloud. But even then it's not really erased-- it lives instead in the Recently Deleted Album in all the Libraries for a about a month. You can see it and restore it any time up to 30 days and then, pffft, it's gone forever. If you want to get rid of it immediately, you need to go to the Recently Deleted Album and delete it there. It will ask if you are sure.

Why are you asking? Are you trying to save storage on your Mac, but keep the photos in iCloud?

If yes, then you must not delete any photos you want to keep in iCloud Photos, but enable "Optimize Storage" in the Photos > Preferences > iCloud. The iCloud will automatically remove high resolution originals from your Mac and replace them by smaller, optimized versions for browsing. Photos will optimise older photos, that have not been used in a long time first, but keep the most recently used photos downloaded. This is fully automatic. You cannot control, which photos will remain downloaded.