Doorways are simple HTML pages that are customized to a few particular keywords or phrases, and they are programmed to be visible only by specific search engines and their spiders.
These pages are designed for one purpose and one purpose only: to trick the search engines into giving them higher rankings. Doorway pages should be avoided, since search engines are pretty savvy when it comes to figuring out if these are being used or not.
Splash pages are intended to be entryways into your site. They usually consist of really neat Flash or other multimedia animation, and may (or may not) invite the user in to the rest of the site when the animation or other such cool stuff is over with.
These pages look really neat, but for the most part, they have no significant text for spiders to crawl (and remember, content is king in search engine optimization).
Not every Joe Browser is able to view the content the way it was designed to view. It's best to stay away from splash pages and focus instead on optimizing your site's content and site design.