An (electronic) mailing list is a distributor of mails to a large group of subscribers, one possible type of a digital forum. It's often used by software developers and administrators for communication among themselves and by organizations and corporations for newsletters (in one direction only).
On discussion lists, every subscriber (member of the group), or at least a group of verified subscribers are allowed to send mails to the list and receive all mails from others. Public Archives (often available as websites) can be either public or non-public.
Announcement lists work only in one direction. An organization or a corporation can use an announcement list (where all customer's mail addresses are collected) send them newsletters. The receivers have to be clients or supporters of the sender and are not allowed to send mails to the list. Announcement lists are also used in software development to inform their users about updates.