the_author() function comes from get_the_author() function that echoes the author of the current post.
the_author_link() function displays the author's website URL as a link and the text of the link is the author's name that is written in Profile Display.
The similarity between these two functions is that they both display author's name of the current post. The difference between these two functions is how they display the author's name. the_author() functions display just a name of the author while the_author_link() function display author's name as a link to his/her website's home page.
The author's role in Wordpress is to write and publish content for their Wordpress blog. With the functions like the_author() and the_author_link() the author's name will always be displayed on the page.