Categories and tags, as far as the search engines are concerned are the same. Categories here though are a post organizational aid so that you can group your posts by subject and you can also have subcategories.
The tags and categories in the posts link to the wordpress.COM global tags pages. There is one theme here that allows you to hide them in the post area, iNove.
You can also use the center privacy option at settings > privacy (block search engines) and your tags and categories in the posts will then go local to your site.
In some themes you can hide them from the post area using CSS if you get the Custom Design upgrade, but this can't be done in all themes. Some themes lump all the post metadata (date, author, category, tag, and sometimes the "leave a comment" link) into a single CSS selector which means hide all or hide nothing.