Yes, hiding from other groups is controlled by editing the forum, and properly using the Group Mode setting. For me, I hide forum post by using "Separate groups." (see Common modules settings graphic.)
If I wanted to hide the entire forum discussion from different groups, I would use the "Restrict Access" feature of the forum, and set this to hide for all except a specific group.
Moodle's "group" features are much more powerful than any other LMS, but there is still always an opportunity for improvement.
