WordPress.com is the free hosting service provided by Automattic. They provide you with free WordPress blogs under the WordPress.com name. Your blog may be something like http://example.wordpress.com instead of your own domain like http://example.com
WordPress.com is a great service for most people to start a blog, but it is limited. Even though they offer special premium services, the service is still limited in some ways. This is where WordPress.org comes into play.
WordPress.org has huge advantages over WordPress.com. You can install any theme you want or you can code your own, or pay someone to build one for you. You can also install any of the plugins available on WordPress.org or third party websites, and you can use your blog or website to advertise or sell anything you want.
WordPress.org is the free and open source version of WordPress. It is an application that you install on your own webhost and configure it just the way you want it to run your website and blog.
Many people start out on WordPress.com and over time, they decide to move over to WordPress.org. This video walks you through moving from WordPress.com to WordPress.org using a webhost that uses cPanel.
This happens to be one of the more popular WordPress tutorial videos I’ve made because so many people want to move from WordPress.com to their own self-hosted WordPress.org installation. The video covers most of the steps you’ll need to move over, you can also watch it on Youtube.