WordPress is a CMS developed in 2003 by Matt Mullenweg and Mike Little. WordPress was the successor to the blogging tool b2/cafelog. May of 2003 was when the first version of WordPress was released. In January 2004, WordPress began a tradition of naming its major releases after famous jazz musicians with version 1.0 being named Davis after an American trumpeter named Miles Davis.
WordPress.org is the free, open source, self-hosted option of running a WordPress website. You get full control over your website. You can install themes, plugins, and modify the code however you like. The downside is you will have to host your WordPress site yourself, and you will be responsible for managing the security, updates, and backups for your site.
WordPress.com is a fully hosted platform. It is a for-profit, paid service that is powered by the WordPress.org software. While it takes care of hosting, security, and updates for you, you do lose some freedom when opting for the paid version of WordPress. The level of customization usually depends on the plan that you choose. Free and lower tier plans have limited access to themes and plugins, while higher-tier plans offer more flexibility.
WordPress is an open source CMS that was developed in 2003. WordPress.org is the completely free, self-hosted option of running a WordPress website. While you have more freedom, it comes with the cost of paying for your own domain/hosting and you are also responsible for the security and backing up your site. WordPress.com is a fully hosted platform powered by the WordPress.org software. The level of customization you have with WordPress.com depends on what plan you choose to pay for. There are a lot of factors to consider when determining which option best suites your needs.