As far as a user was concerned, before Mac OS X, the Finder's icons and the files they represented were one object, as were the Finder's windows and the directories they represented. However hard you tried (which you didn't, because you knew a file was the same as its icon), each file had only one icon and each directory only one window. Also, each directory/window had its own position on the screen, size, and layout.

Now, that 1:1 identity is broken. You can have multiple windows showing the content of the same directory. Also, you can have multiple icons on screen 'pointing' to the same file.

This may look like a minor change, but the feel of the UI is very different. It feels much less a direct manipulation interface.

Yes, Mac OS already was slightly inconsistent. Open and save dialogs could show directories and Windows that wer visible in the Finder. However, these felt as part of the application, and were very focused on the task at hand. Icons in those dialogs felt as representations of files, not as the files themselves. Also, there were aliases, but being files, they maintained the 1:1 correspondence between icons and files. Altogether, those things never killed that illusion of 'an icon _is_ a file, a window _is_ a directory'.

Because Mac OS X is a multi-user system, I think Mac OS X had to break this rule (network shares were already stretching the metaphor (almost) beyond breaking years before Mac OS X), but even today, it still feels like a loss to me.