This breaks down to three levels.  There is:

• Per forum, set in your My Settings, or in threads view.  You will get an email, when enabled, when any new threads occurr or new posts are added to existing threads (only once approved).
• Per Thread, set in Post or Post Edit View.  You will get an email when a specific thread has any new approved replies.
• The third level is actually broke due to a bug in the core, and this is when you have a notification forum, set at the forum management level. 

This is exactly as any forum app I have ever used works.  If you still require answers, please see the modules documentation.  I do see your point about the label being somewhat misleading though.

Question!  I would like to start helping with the online forum module.  How do i get the newest version that is under development.  I realize 3.20.1 is the current version, but i would hate do to work that has already been completed. 

Thanks for your help.

Tim