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In both scenarios you still need to set up, manage, and host a CMS somewhere.
In a dynamic scenario (also referred to as a monolythic system), your page request typically reaches the CMS itself (or a caching layer), and the CMS decides exactly what to render and send back to you based on your authentication status and possibly other criteria.
In a decoupled scenario, your page request reaches an HTML page that then, in turn, uses JavaScript to communicate back and forth with a CMS to fetch and display the requested content.
Image: QED42