WordPress.com is hosted, free and contains restrictions on what you can and can't do. When you comment on other people's blogs you use your username and link automatically back to your profile. WordPress.org is free as well, but you install on your hosting and extend, use, etc any way you want to.
We're both right and wrong and here's how I justify my answer. Wordpress.com will give you the hosting and domain, which makes no cost to you at all, none. In order to use Wordpress.org, you need to pay for hosting and your domain (which doesn't really make it free). You can certainly download Wordpress.org for free, but what can you do with it without paying for the hosting and domain? Wordpress.com vs Wordpress.org
In Wordpress.com you are not in control but in wordpress.org you are in full control. You can do what you want with it.