A discussion list is like a forum for information exchange on a specific topic.
Mailing lists work like a distribution service of e-mails.
There are different ways to handle mailing lists, which depends on used server software. Some lists have WAIS searchable archives of discussion threads. Newsgroups are like electronic bulletin boards, no subscription necessary, but also no list of potential users available. I don't give here my own list of mailing lists for statisticians, but you'll find some web sources with lists including details and joining information. Best collection, by Mike Fuller.