Explain the_author() Function
This function is used to display the name of the author of the current post. However the true intent of the function is to echo the author but not necessarily return it.
Explain the_author_link() Function
This is used to retrieve either the author's link or the author's name. The result will echo an HTML link if the author has a home page set or it will default to echo the author's name if no home page is set.
Explain Differences and/or Similarities
In both functions WordPress is identifying the author of a post. In the_author() function WordPress will simply retrieve the author's name from the post. However in the_author_link() function, WordPress can retrieve a HTML link to a home page if set or simply retrieve the author's name if no page is set. If a page is linked, the post will still display the author's name, but it will appear as a clickable link.
Summary
In my opinion, with a little extra styling, I think that the_author_link() function maybe the better way to call for the author of the post. I think the added benefit of linking to a home page and defaulting to simply the author's name if a page isn't set sounds like the better way to go. It seems more user friendly. Especially since a user may want to find out more about an author on a post. This seems like an easy way to do this.