_author() Function

Using the above function displays the name of the author as a string in the current post. It originated from get_the_author(), and has deprecated parameters, as it used to not return the value of the author, but only echo it out.

_author_link() Function

The function above retrieves the author's home-page, if set up, otherwise, it will return the author's name. When a page is built, dedicated as the author's homepage in WordPress, the _author_link() function will echo out the HTML link.

Differences & Similarities Between Both Functions

While both functions can echo out the author's name, _author() strictly echos the author name, while _author_link() will echo an HTML link to the author's homepage, if present. If the homepage is not present, the function will instead echo out the author's name.

Summary

Using the _author() and the _author_link() functions can retrieve the author's name of a post and echo it out on the page. In the case of _author_link(), if a page is set to be the author's homepage, it will instead echo out the HTML link to that homepage.