What does Group Type = Mailing List do?
I think I have discovered the answer to this.

If the 'Mailing List' box is ticked and the visibility is set to public the group is listed on a page (yourdomain.org/civicrm/mailing/subscribe) that allows people to subscribe to the mailing list.  If the box isn't ticked it won't be displayed on this page.

It doesn't appear to affect whether the group can be used to select recipients for a mailing, which is what I first thought it did.