www.ads-software.com Vs WordPress.com

I am very new to web hosting and from what I understand when it comes to WordPress, there are 2 different sites WordPresss.com- with this you are only responsible for the content and they do all of the hosting and setup.

With www.ads-software.com- you get the open-source WordPress software, you are responsible for finding your own host or hosting it yourself and setting up the installation, security ect…

I have also heard that with wordpress.com you dont get all the customization and plugins that you would have with your own host like (hostgator) and www.ads-software.com.
Is this true?