WordPress History
WordPress was originally created as a tool to publish blogs. It was created by Matt Mullenweg. WordPress was originally realeased in 2003 as a free opensource project that eventually evolved into a content management system. It is one of the most widely used CMS on the web today.
WordPress.org Entity
Wordpress.org is the completely free open source version of Wordpress. It allows for users to self-host their site, and maintain complete control of their content. The user has complete access to all files and code. The user is responsilbe for the maintinance of the site. WordPress.org is managed by the WordPress Foundation.
WordPress.com Entity
WordPress.com is a web building platform. It is a free blog hosting platform, however it does offer paid content services. WordPress.com is owned by Automattic. It is the for profit version of WordPress. It was created in 2005. This version of word press is web hosted.WrodPress.com will take care of the management of the users site.
Summary
Together WordPress.com and WordPress.org offer the user the opportunity to create a WordPress site. The free self hosted end of the .org and the paid for profit web hosted site of .com. The choice depends on the users needs and demands. It boils down to the simple premise of hosted or self-hosted and the amount of control the user wants to have over the design and management of their site.