I think you have that absolutely backwards. The difference between Bootstrap and a CMS is that a CMS is an application. Bootstrap is purely a sort of standard UI toolkit for the web.
A pre-requisite for being a CMS is managing content (Content Management System). Bootstrap has no content-managing facilities; It is purely a presentational (CSS, some JS) library with some well thought out defaults.
ie: you could still use Bootstrap to style a WordPress site.
I think "backwards" is the wrong word. I'd say "uninformed" would be closer to the point.
CMSs manage your content usually through a database, and most of them provide a way to display that content in a structured format. See Wordpress and Drupal. WYSIWYG is not a necessary part of a CMS.
Bootstrap is a (mostly) css library to help provide a better front end development experience for a web site/app. It can be used with the front-facing portion of a CMS or any other kind of site.
