Today, I found this amazing post:
from codeinwp.com website by Karol K.
She resumed clearly what the difference is:
WordPress.com
is an online platform where you can go, sign up, and create your website/blog all in one place.(To give you a clever comparison, WordPress.com is your Google Docs (bear with me).)
WordPress.org
is an open source software. To launch a website with it, you need to first download the software, and then install it on your own web server (or a web server you’re renting from a third-party).(Continuing my “clever” comparisons, WordPress.org is your Open Office / MS Word.)
Read a more in-depth post here: http://www.codeinwp.com/blog/wordpress-org-vs-wordpress-com/