Icloud for new Mac mini

Cloud Photos is a synchronization service. When you engage iCloud Photos on a device, then the Library on that device is kept just the same as the iCloud Photos Library. So, for instance, if you take a picture with your iPhone, it is added to the iPhone's Photos Library, copied to iCloud Photos Library, and then copied to the Photos Library on each of the other devices that you have connected. If you delete a picture on your Mac, then that picture is deleted at iCloud and on all the other devices.

It sounds like you want different pictures on different devices, so at least one of them must be disconnected from iCloud. Do you want the 2004 Mac to not have any newer pictures? Then do this on the 2004 Mac:

1. Duplicate, ⌘-D the Photos Library, probably named "Photos Library.photoslibrary" that's in the Pictures folder
2. Put the duplicate somewhere safe, perhaps as a backup on an external drive, but make sure the duplicate is removed from the Pictures folder.
3. Make sure the remaining Library is still designated as the System Library in Photos' Settings>General, and connected to iCloud at Settings>iCloud.
4. Then delete all the pictures in it.
5. They will then all be removed from iCloud. It may take awhile.
6. When you're sure iCloud is empty, delete the empty photoslibrary from the Pictures Folder

You can copy that duplicate Library back to the Pictures folder, and make sure iCloud is off. Then you can double click on it and have the old Library back, but only on 2004.

Make sense?