The 3 modules are different:
- The Sharing module allows you to add sharing buttons at the bottom of your posts. You can add as many sharing sites as you want there, as explained here: http://en.support.wordpress.com/sharing/
- The Publicize module allows you automatically post to your favorite Social Networks when a new post is published. You can find out more about it here: http://jetpack.me/support/publicize/
- The Enhanced Distribution module is used to share your new posts with third party services such as Search engines. This module doesn't need to be configured, and uses the WordPress.com firehose.