You need to pay for both domain mapping and domain registration (holding) no matter how you set your blog or site up - some hosts don't charge for domain registration as a separate line item but build the "free registration" into the cost of the hosting. If you host not at WordPress.COM the cost of the domain mapping is built into the cost of the hosting. The reason there is a domain mapping cost at WordPress.COM is because the hosting is free and then you pay for upgrades from the base cost of $ 00--.
Registration at WordPress.COM is $ 5-- / year. the other options are for Domain Mapping and Private registration (your registration information is hidden from the public - $ 8-- / year I think)