The function "the_author()" is a PHP code function used to display the name of the author who wrote the current post on the page.
The function "the_author_link()" is a PHP code function that is used to display the name of the author for the post but will also can make the name a clickable link to the authors website URL if set.
The functions, "the_author" and "the_author_link" are very similar in that they will both display a post authors name. However, "the_author_link" takes it another step, with making the authors name a link to his or her website url.
Author functions are a very useful tool in WordPress and CMS. It is an easy way to dynamically pull the names of authors from the database and display them for the users to see. "the_author_link" would be especially helpful if an author has their own URL and a user wants to look them up to research more into their work.