I may be misinterpreting your question, it could use some more detail, but I think the old site must have had a plugin installed. Posts and their statuses are not displayed in any of the default WordPress dashboard widgets.
The only two plugins that I know that do something like that are Post Status Menu Items—by pure coincidence, I’m the author of that plugin—and EditFlow. I’ve included a screenshot of those two side-by-side, respectively.
