The difference between private and private (hidden) is basically that BOTH can only be accessed by users who have been given permission to do so but HIDDEN can't be seen on the forum index.
As for your private forum for a group of members - go to your admin page:
1. Make the forum PRIVATE in forum permissions (or PRIVATE (HIDDEN)).
2. Select "Management" from GROUP ADMIN.
3. Create New Group.
4. Fill in the details (Open group means users can request membership via USERGROUPS option, closed means they can't, Hidden means they can't see it in USERGROUPS).
5. Select "Permissions" from GROUP ADMIN.
6. Choose your group and LOOKUP.
7. Find your "private" forum. You will see an option under the SIMPLE PERMISSIONS column - Allowed Access / Disallowed Access.
8. Select ALLOWED ACCESS.
------This will setup a usergroup that will enable you to add members to it. When you add the members to the group, they will have access to the private forum-----
9. Go to the forum index (not admin).
10. Click on USERGROUPS.
11. Select your group.
12. Add members who you want to have access to your private forum.
-----This should be all you need-----