I think I understand it all a little bit better.

A WordPress blog can either be structured as a page based website or its conventional post based structure can be retained. That’s why understanding the differences between posts and pages, http://en.support.wordpress.com/post-vs-page/ comprehending the SEO implications of creating a page based structure, and knowing how to use custom menus http://en.support.wordpress.com/menus/
are key to decision making when selecting a theme, and setting up your WordPress.com blog. http://onecoolsitebloggingtips.com/2010/05/12/better-blogging-at-wordpress-com-pages-and-posts/

On one hand, none of the characteristic "blog" features likes categories, tags, authors, dates, etc. can be removed from a free hosted WordPress.com blog without purchasing an annually renewable custom design upgrade and doing the required CSS editing.
http://en.support.wordpress.com/custom-design/
http://en.support.wordpress.com/custom-design/#frequently-asked-questions
http://en.support.wordpress.com/custom-design/editing-css/

On the other hand, one can hack a WordPress.org theme free of charge. Have you read this comparison? WordPress.com and WordPress.org: The Differences http://en.support.wordpress.com/com-vs-org/

Thanks for your response! I think I am misunderstanding the word 'blog'. My knowledge is that it is almost like a diary in which I can write and other people can read it. For example if I want to give fashion advice to my readers.

I don't want to do that. I just want to purchase a .com domain and design a website with the available themes for my business.

Apologies if I am repeating or misunderstanding your response. This is all new to me.

If you’ve registered your domain through WordPress.com and now later want it to point to a blog or website hosted elsewhere then you can do this by updating the nameservers. http://en.support.wordpress.com/domains/domain-management/#update-nameservers