In short, WordPress.com is a WordPress hosting business. You are only responsible for the content. They take care of everything else like setup, maintenance, and security updates. WordPress.org is for the open source WordPress software. With WordPress.org, you download the software, choose your own host(like x10), and are ultimately responsible for everything regarding the installation and maintenance, backups, security updates and customization.
Which way you choose to host your WordPress site depends on what you want out of it. Since WordPress.com is a business, they put limits on their free plans(like creating a custom theme, installing plugins, or using your own domain name) in order to entice customers to upgrade to paid hosting plans. On the other hand, if you host WordPress yourself, you have full control of all available features straight out of the gate for no cost at all, not counting any fees you may have from your web host.
Are you just hosting a small personal blog without the need for some features of a full WordPress installation? Or, are you willing to pay for some features rather than worry about a lot of the setup, maintenance and updates for your site? If so, then WordPress.com might be a good option for you.
If you don't mind getting your hands dirty and would rather do all of your own maintenance, setup, and troubleshooting in return for free full control of your site, then self-hosting is the way to go.
I hope this helps,