Absolutely not. WordPress.com is clearly separated from WordPress.org. What you get with WordPress.com is that they handle all server admin, themes, plugins, site installation, and so forth. This is great for beginner users, because they often cannot handle normal hosting tasks, and cannot fix a problem when it arises.
And if the users want extra stuff, they pay for it, and WordPress.com makes a little money. And given the extremely variable quality of free themes, there's no way in you-know-where that WordPress.com can guarantee that they'll work, so they feature themes that do work reliably.
WordPress.org offers much more flexibility. You can control every aspect of your site, including the theme, because you are hosting the site somewhere, like Liquid Web or elsewhere, the WordPress people are not hosting it. So the price for this flexibility is that you need to handle everything about the site yourself - geek skills are a must!!! Beginners get excited when they see free stuff, themes, plugins, and so forth. But then they are often disappointed, because something doesn't work, their site has been hacked, some theme looks funny, and so on, and they have no clue how to fix it. They don't need to worry about this stuff with WordPress.com.
The unfortunate thing is that Godummy and other hosts are now offering 1-click installs of WordPress (the .org version). This sounds great, but then the person installing it has no clue how it works, or even the simplest tech skills needed, like FTP, file permissions, etc., so it becomes a tech support nightmare.
For beginners, with no geeks helping them, I recommend wordpress.com, because quite frankly, as I see every day in the forums here, beginners are not capable of handling all aspects of hosting a site. If you have strong geek skills (that leaves out probably 90% of WordPress users) and want all the control that this allows, WordPress.org is the way to go.