Ideally those can be the same thing; see the current Mailman interface, or Discourse, both of which can provide a forum-like interface to a mailing list.
Forums are more for new and normal users/fans of open source projects. Technical discussions happen over IRC. And even more longer insightful technical discussions (often over several days) happen on mailing lists.
This is true for large open-source projects but there are plenty of µframeworks and tiny Unix-philosophy-following tools that don't need more than a Git(hub|lab) repository with the issue tracker enabled.
And almost all do. Even newer ones like Elixir that started with Slack have now a mailing list and an IRC channel.