Just like a library, the Web contains information of different types that is stored and retrieved in different ways. The content of search engines on the Web is itself stored in databases and available only through user query. The logic of this terminology just doesn't hold up. This is much better since database content is visible with the appropriate search and retrieval technology. This can include large listings of things with a common theme.
All directories are part of the deep Web.
Information that is new and dynamically changing in content will appear on the deep Web. A good subject directory will link to database sites on the Web. This is because many of these databases have Web sites of their own. For example, you can go directly to the Moreover site and browse its datatabase of current news stories. A directory, therefore, can link to the Moreover site from its news section.