The right terminology is Top Management Consulting or Strategy Consulting. They are board advisors at heart, and they help C-Level executives plan and execute their business strategies (where to play, how to win, how to transform the business)
This is different from Management Consulting because this one caters mostly to middle-management issues (i.e. running the day-to-day business, operational improvement).
Please note that not only MBBs do strategy consulting, Tier 2 consulting firms (focusing on top management consulting) do that as well.