When we search Wordpress on Google Search, we will see two website: wordpress.com and wordpress.org . I normally use wordpress.org for my post. So I will explain the different is of wordpress.com and wordpress.org
- What is wordpress.org
Wordpress.org is a website page of Wordpress Open Source, you can download Wordpress code in here and install your hosting, set up, and manage your site. The automatic install Wordpress is called Wordpress Seft-Hosted
I recommend to use Wordpress Seft-Hosted, because you can manage all Wordpress. You can set up, install, use your domain name, set up theme, install plugin by your-self.

- What is Wordpress.com
Wordpress.com is a website address of free blog service use Wordpress. This is the service of Automatic but this is for normal user who want to have a Wordpress website with few click without setting, and host service. The service of Wordpress.com is 25 USD/year for one website.
With Wordpress.com service, you cannot install theme by yourself, you only use the free them on Wordpress.com. You cannot only install plugin by your-self, you must use the basic function on Wordpress.com. If you want to change from Wordpress.com to Wordpress.org, please click this instruction.

Summary
If you want a Wordpress Blog with few click, let focus on Wordpress.com. If you want a website that design by yourself, let go to Wordpress.org