In Directory submission, you are submitting your site to the Directories.The directories are easily get noticed by the search engine.Its easier to get Google crawling.Once Google crawl the directory means all the sites listed over there get the crawling. Search Engine submission is the method of submitting the site to the search engine.Usually its not requires as all the search engine get the Bots to do this work.But in some cases the search engine take time to index the site or if you want to get noticed by the search engine, this method is required.