To have Discourse comments show up on your WordPress site, you must select the Enable Discourse Comments setting. When enabled, you will see two options. The Display comments option will load a Comment template for each WordPress post that has been published to Discourse. This template will display Discourse comments beneath the WordPress posts. The Display a link to the comments option will load a comments template that displays a link to the associated Discourse topic underneath the published posts. The number of replies to the topic will be displayed in the link, but no replies will be displayed on WordPress.
Both of these commenting options work by loading comment templates for the WordPress posts. This means that they will only work if comments are enabled for the post. If you would like to enable comments for all posts, but not have any historical WordPress comments be displayed for posts that have not been published to Discourse, enable the Remove WordPress Comments Template setting.