A mailing list is an email address which can forward emails to a group of people. Mailing lists do not necessarily forward all email, frequently there is an automated or manual approval before forwarding happens.

A mailing list manager is a person or program which maintains one or more mailing lists.

An automated mailing list manager is a mailing list manager which is a program. Examples of programs which may be used for this include mailman, sympa and ezmlm.

Note that I made your "moderated" piece optional. While public mailing lists tend to be moderated, many private ones are not. For instance most of the mailing lists which I am on at work are not moderated - anyone who knows the address can send any email they like to the group.

Cheers,
Ben