What's the difference between a Contact and a Connection?
This article defines Connections and Contacts and explains the different privileges and options available for each.
Contacts are all the people in your Yahoo! Contacts (previously called Yahoo! Address Book).
Connections are Contacts with whom you have a privileged relationship. These Contacts can view your personal Updates, such as birthday reminders and changes to your contact information. Email from your Connections is prioritized in your Yahoo! Mail, and both you and your Connections have access to more information when viewing each other's Profiles on Yahoo!.
To learn more about transforming Contacts into Connections or inviting friends to connect, please visit the help article, "Sending and Requesting Updates and Invitations to Connect with Yahoo! Messenger".
Note: when you invite someone to connect, you will automatically begin receiving their public updates, whether or not they decide to accept your connection.