One of the nice things about Linux, though, is that you can move or even remove something with an open file handle on it (but not a mandatory lock, though these are rarely used) without invalidating the file handle. In the case of moving a file, the file handle continues to point to the moved file. The old path isn't valid, but once the file is open, the path doesn't matter. In the case of removing a file, the file handle remains valid, but no new handles can be opened and it wont show up in listings. Once the last handle is closed, the file is finally removed.
Windows is quite a bit more anal. Both options have their advantages and disadvantages. In the face of poorly written software which sometimes closes and re-opens a file for writing upon "save" using the original pathname, the Linux (used by most UNIXes) can result in files showing back up with new content (and the moved file having the old content), and I think there are a lot of Windows apps that do this, so I can guess that's why MS has stuck with their current approach since forever. That may also be the way VMS handles it, and NT is based upon VMS.
Incidentally, simply performing an action on a file in Linux won't tell you what processes have a handle on it. You need something like lsof to tell you that, but said command is pretty common. Some GUI file managers may implement this function for you.