login_footer in wp-login.php

Generally, home_url is where the site exists (the site’s home page), while site_url is where the actual WordPress installation exists. Usually they’re the same. Since this is for a link to the site’s home page, home_url is the proper template tag.

Function Reference/home url
Function Reference/site url

I understand the difference between site_url and home_url.
I noticed that the text of the anchor is the title of the WordPress blog – not the name of the site (the website’s home page) … so shouldn’t the link go to the WordPress blog.
Alternatively, if the intention is that the link should go to the website’s home page, then the text should be changed to reflect that.
My point is that the anchor href link should go to the place described by the text of the anchor … and this is not happening at present.

home_url points to the main front-facing page of the installed WordPress blog. The link in question is intended to return any errant visitors to just that page. I fail to see the problem with “Return to Example” linking to example.com.

For example, if I install WordPress into its own directory (example.com/wordpress) but then set it up so that the actual WordPress site is displayed at the root (example.com) then home_url will point to the proper example.com while site_url would point to the publicly non-existent example.com/wordpress.