Wordpress-what is it?

WordPress is software designed for creating and maintaining blogs. It has special applications to support editing and publishing blogs. Wordpress has been around since 2000 and is used by well known businesses and non-profits. WordPress has a rich text editor with advanced multimedia support and is free to use and distribute. 

WordPress.com is free blogging software that hosts the site on their servers. All you need to do is register and then launch a blog. It is important to note that Adsense, Yahoo, TextLinkAds and other ads are not allowed on WordPress.com blogs. They also do not allow sponsored reviews and many affiliate and referral links. If you plan on monetizing your blog don't use WordPress.com. 

WordPress.org is a stand-alone version of the same software that you can download and install on an independent web host. The software is free all you need to provide is a domain name and host. They have partnered with some hosts such as GoDaddy and these sites offer an easy install button for WordPress. If you’re not picking one of the recommended hosts just make sure the host is running up to date versions of PHP and MySQL. These will allow your WordPress installation to work on that host. Set up is easy using Fantastico. 

You can find the Pros and Cons of each according to WordPress here.
Notice they don't mention anything about not being able to monetize your blog on WordPress.com in the Pros and Cons section; you need to look a little further to find that. WordPress.com is a great way to start a hobby or special interest blog, but for a small business it is very important to have more control over the website.