I know it is confusing, someone perhaps can tell me how to name the two "groups" we have in fop2.
You are confusing one with the other. What you want is to visually group buttons on the screen, lets call that "visual groups". A visual group is configured in the FOP2 BUTTONS page, you have a field for each extension named "group", just write whatever you want. Extensions with no group defined will be displayed in the Extensions box. If you write "ZZZ" for some extension, a new box named ZZZ will appear on screen containing that extension or any others with the same group.
The other group feature is what you can define in the FOP2 GROUPS menu. This lets you limit the display and actions to a particular subset. Then, you can assign these groups to a user, and that user will only be able to see the buttons that are part of the groups it has assigned. We can call this something like "Filter Groups" if you want. This groups can also be used to limit your custom permissions to a subset of buttons. They do not affect your visual grouping in any way, they will just filter out whatever is NOT part of the group you have assigned if you have some groups assigned.
Best regards,
