WordPress.com
“Focus on your beautiful content, let us handle the rest.”
The main focus of wordpress.com is that all the technical stuff is done for you. You don’t have to worry about all the maintenance and backups as these are done for you. There is also a large amount of themes to choose from so you don’t have to worry about making one. There is less need to install as many plugins with WordPress.com.
WordPress.org
“Get your hands dirty, and host your website yourself.“
With this one you’ll need to do everything yourself. You’ll have to find yourself a host and perform maintenance and backup yourself. There are a number of plugins available to help with this.
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