A wordpress theme uses the content managing system (cms) Wordpress which is probably the easiest and most powerful blogging and website cms in existence today. And it's open source, which means it is free.
You don't need any coding skills because it is fairly easy to use. You receive an installable theme zip file.
As the name suggests, templates are developped in HTML code, css and javascript. This means, you need at least basic coding skills to edit the template and adapt it to your needs.
When buying a HTML tempalte you receive the raw html/css/javascript files which you edit with any text editor.