if ( is_home() && ! is_front_page() )

I see the following code a lot in index.php files. I understand that is_front_page() returns true when viewing the Site Front Page (whether displaying the blog posts index or a static page), while is_home() returns true when viewing the Blog Posts Index (whether displayed on the front page or on a static page). I am still somewhat stumped about the use of the following code –

Custom columns on edit-tags.php main page

I am trying to add custom columns to edit-tags.php for a custom taxonomy that I have created. This custom taxonomy is called equipment-types and it only applies to one custom post type called equipment. I am trying to use the same filters and actions that I would use to add custom columns on the edit.php page. I was able to actually create the custom columns with this filter: