Call Display, CID, or Caller ID are often used synonymously. They refer to the number displayed to the receiving party as well as the text or CNAM which is sent to the receiving party with the call.
Commonly formatted as a name and number like this:
Call Display can be overridden on the receiving party phone if the phone has an address book with a matching entry for the phone number.
Passing the name between phone networks is supported however due to the large number of network interoperators, the name may not pass through all the time. Some cellular networks are starting to support passing names as well.
Related Knowledge Base Articles:
External vs. Internal Call Display
Requesting a change to Call Display