WordPress.com is a blog network run by Automattic. It uses WordPress software, but individual blogs are hosted and managed by WordPress.com. This is a free service with premium addons and upgrades.

Here at WordPress.org, you can download WordPress, the web software that WordPress.com runs on. Once you’ve downloaded it, you can upload it to a web server and run your own WordPress website.

There is useful information about this distinction on the WordPress.com website.