I like things simple, so I found this great infographic on WPMU.org that illustrates the difference between WordPress.com and WordPress.org.
My only disagreement with this infographic is the price for hosting a WordPress.org website. Make sure that whatever host you choose offers “managed” WordPress hosting. That means that their servers are optimized for WordPress, they guarantee security (you won’t get hacked), they back up your site nightly, and update your core WordPress files automatically. As an added bonus, managed hosts are usually much faster at serving your website, as well. A managed host will give your website a safe and secure home, and you some peace of mind.