Web Directories have real live people reviewing sites that were submitted. Search engines send out robots to index the site.
In order to have your web site accepted by a Web Directory you need to submit the site on-line. At some point a directory editor will visit and evaluate your site. They then decide whether or not your site will be included in their directory. Once a web site has been accepted it is listed in a specific category. Users can browse through these categories or search using a keyword.
The search engines use robots which are automated software called spiders and crawlers to index your web pages. The information that is collected is then placed in the search engine's database.
When a user queries a search engine the search for the queried information is done on the search engine's index and not the actual web.