the_author() displays the author's name of the current post. It can also echo the value from get_the_author().
the_author_link() gives the author the option to post a hyperlink.
Both the_author() and the_author_link() display the author's name, however the_author_link() allows the author to add a link to their home page in a way that the_author() cannot.
The default post behavior is to display the author's username, which is typically not ideal. It is better to use either the_author(), or the_author_link() if the author wants to include their own link.