This kind of automatic comments are called "trackbacks" and "pingbacks". They are a blogging feature that consists of automatically notifying blogs that are linked to from an article when said article is published.
This notification appears as a kind of comment on the mentionned article, with a link pointing back to the newly published one.
Specifically in the case described in the question, this is a "self-ping" (as in within your own site).
You can disable both emitting and receiving trackback in WordPress as follow:
To stop emitting trackbacks and pingbacks: Settings > Discussion > Default Article settings: Uncheck "Attempt to notify any blogs linked to from the article
To stop receiving trackbacks and pingbacks on future articles: Settings > Discussion > Default Article settings: Uncheck "Allow link notifications from other blogs". This setting will serve as default from future article, but does not affect existing articles.
To stop receiving trackbacks and pingbacks on existing articles: You can disable trackbacks for each article individually just like you can disable comments. From the edit screen, hit "screen options" at the top right and make sure "Discussion" is checked. Scroll to the "Discussion" box below the content editor, you'll find two checkboxes to enable/disable comments and trackbacks, respectively.
To only prevent self-pings without disabling trackbacks and pingbacks to/from other blogs, the solution is to use relative URLs in your post when linking to other posts on the same site (as opposed to absolute urls starting with http)
Reference and more information: https://make.wordpress.org/support/user-manual/building-your-wordpress-community/trackbacks-and-pingbacks/