What’s the difference between WordPress.org and WordPress.com?
WordPress is open source web software that you can install on your web server to create your website, blog, community or network. WordPress started out as a tool for blogging, but has evolved into a full-fledged Content Management System (CMS), capable of powering websites, networks and communities.
WordPress.com is a blog network run by Automattic. It uses WordPress software, but individual blogs are hosted and managed by WordPress.com. This is a free service with premium addons and upgrades.
At WordPress.org, you can download WordPress, the web software that WordPress.com runs on. Once you’ve downloaded it, you can upload it to a web server and run your own WordPress website.
There is useful information about this distinction on the WordPress.com website.