TL;DR
Simply put, WordPress.org (or just WordPress, really) is the open-source content management system itself (CMS).

WordPress.com is a commercial service that allows you to create a WordPress website with a few clicks. Automattic, the company behind WordPress.com, took WordPress the CMS, built a platform around it to create a product named WordPress.com.

What is WordPress(.org)?

WordPress is the world’s most common open-source content management system. The project’s homepage is WordPress.org, where you can download the WordPress core files, plugins and themes as well as read documentation on the CMS.

In order to run or create a website using WordPress, you will need to get a domain name, a web hosting account and install WordPress there. When WordPress is self-hosted, you have full control over all aspects of the site; You’re able to install any WordPress theme or plugins and your (or your developers’) skills are the limit to what you can do with your WordPress site.

What is WordPress.com?

WordPress.com, on the other hand, is a platform that offers WordPress as a one-stop shop; You don’t need to get your own hosting or domain, because all of that is offered as a part of the WordPress.com service.

On WP.com you’ll be restricted to a certain set of plugins and themes. While their selection is great, the options are fewer than the total number of plugin and theme choices out there.

One way to look at the difference between WordPress WordPress.com would be to compare going to a restaurant and ordering from the menu vs. going to the grocery store to get ingredients and do the cooking yourself.

Technically, you could create your own platform like WordPress.com. If you had the resources, you could build the infrastructure and become a “WordPress-as-a-Service provider like Automattic, the company behind WordPress.com.