This post clarifies this issue for any who do not know the difference.
WordPress is a PHP/MySql based content management system that you can download and install on your server. It is hosted at wordpress.org. At this site, there is a support forum to help you solve problems that you are having.
But at wordpress.com you can obtain a free blog which is powered by wordpress but which is not customisable to any level. You can choose from a variety of themes, but even after paying a fee you can only change the CSS.
WordPress.com is good cheap option to get you started, but churches should have their websites hosted elsewhere where they can customise it. But most importantly, so they can get a custom domain… http://www.mychurch.org.uk, rather that mychurch.wordpress.com
The church website that has been set up uses the wordpress code on its own site wordpress software, rather than being hosted on wordpress.com.
Update: wordpress.com now allows sites hosted to pay and use their own domain so one of the points above is not so relevant. However, they can only register .com domain names and no others, which is a bit of a problem for UK based charitable organisations.