the_author() function.
the_author() is designed to echo the data retrieved with the get_the_author
function. It returns the author of a posts name. If the author is unknown an empty string is returned.
the_author_link() function
The the_author_link() function echos either the authors home page if one is set, or the authors
name if a homepage is not set.
While both functions can echo the authors name, that's all the_author() will return. While
the_author_link will by default return the authors homepage and not their name unless no
homepage is set.
So if you only want to show the name of the author use the_author(), if you want to show the
author's homepage then use the_author_link(). If you want to show both, I guess you would
include both functions.