You could achieve that by having each group on a different Theme, with each theme using its own copy of this Theme Component.
This would work nicely if one of your two groups was quite static (or at least smaller) - your staff group seems ideal for that. Or at least if you only had one dynamic group.
You then make the student links the site default Theme, and the make your staff members have the staff links manually (either by the UI or via the Rails Console).