The difference between wordpress.com and wordpress.org:
Wordpress.org is the site that produces and serves the code (the software) for the wordpress blog platform. You can freely get this code and install it to a server/host of your choice and have a blog that is completely owned by you. This is a self-hosted blog where you set the rules of what works and what does not. And there, you have administrative privileges and install whatever you want.
If you want the free stuff though, without the hassle of setting up a server by yourself, you can go to wordpress.com and create a subdomain (like e.g. inlinkz.wordpress.com).
There are paid and free accounts in wordpress.com and the hosting, servers etc is done by them. The drawback is that their blog platform, has some restrictions, one of which is that you cannot embed scripts or objects, thus you can only host a linkup that displays in an external page and not inside your post.