A vanity site is a simple site to give you web presence. Usually one to three pages. Social Media integrated.
Contains four to eight pages. This site is a typical site for personal or small business. More info involved, more features.
Contains many features like email mailing list, calendar, multiple galleries. These are sites that require intensive customization.
Custom Site's are just that. Built from the ground up or so heavily customized they might as well be built from scratch.