With wordpress.com, you get a domain set up like “yoursitename.wordpress.com”. With that set up, wordpress.comcontrols the design and you can’t upload and edit your own design. You have very limited control over what you do and add to your blog. You can google lots of articles on this as well.
With wordpress.org, you can download the open-source software and use it with any theme, like the themes from our shop! In order to do that, you have to have a domain name and hosting. So, wherever you’ve purchased your domain, I recommend getting hosting from the same place. My favorites are GoDaddy and BlueHost.