They are two different things. Not sure why you add b/w because black/white SEO has nothing to do with either. Site directories = e.g. dmoz.org Sitemaps = URLs of your website to help search engines index all
Sitemaps gives the overview of the sit to the search engines. Whereas site directories are the websites where you submit your site links. Both are important for SEO.
The basic difference between both is the source included in it. The site directory contains the names of related sites and details about them. The sitemap shows the flow of links and pages where they have been placed.