WordPress.com is owned by Automattic Inc. and is a paid service the benefit to using it is you can easily start using the platform without worrying to purchase web hosting and domain name, which WordPress.com can provide you on their platform.
Whereas, WordPress.org is open source, they both use the same codebase and are similar whereas in case of WordPress.org you need to download and host the platform on your web hosting account. So, it takes slightly more effort to get started with, but the benefits are unlimited.
Pros of WordPress.com
Easy to start with, ideal for occasional bloggers.
Good for non technical person looking to build a blog.
In-expensive, when considering costs of hosting and domain name.
Cons of WordPress.com
WordPress.com owns some rights and may delete your website in case of privacy violation which means losing all your work.
Limitation on customisation of templates and no access to editor section of wordpress which allows you to make important changes to your website files.
Pros of WordPress.org
Note: WordPress.org is also called Self hosted WordPress.
Self hosted WordPress, is also easy to setup but need slightly more effort that WordPress.com, learn more.
End less and un-restricted rights to customisation of templates and access to editor section of wordpress which allows you to make important changes to your website files, like adding code to website header learn more.
Unlimited free and premium themes, plugins and templates available.
Cons of WordPress.org
None. Its surprising but the reality is self hosted instance of WordPress is highly recommended.