OK, trying to clear up the confusion a bit:
Wordpress.com - Is a free blogging platform that uses the Wordpress software to let you build blogs. It is limited on how you can monetize your blog, but depending on your niche, it is perfectly possible. They don't allow normally Adsense and the like and are very weary about people just blogging for money. But they are ideal for writer's that want to build their portfolio, offer services like editing / proof reading and similar. Danger is, like with any platform you don't own, they can delete your site if they don't like it. For the type of blogs they like/don't like see http://en.wordpress.com/types-of-blogs/
Wordpress.org - is the place where you can get the software Wordpress from in order to use it on your own site. You will also need a domain name like yourname.com and a hosting account. Yearly costs around $100 all included. Then you can build your own blog / website and pretty much do anything you want with it. Including running Adsense and affiliate ads like Amazon.
Hope that helps, if you have questions about setting up your own web site / blogs, feel free to PM me, I have set-up dozens to date, SY