Team Management vs. Influencing

I have been thinking about this a bit, and have come to the conclusion that managerial roles can be classified into two broad cateogories:

• Team Management Roles: These are classical management roles where you have 'n' people below you. As a manager you achieve your goals through these 'n' individuals by appropriately motivating them to achieve their goals, which will cumulatively achieve yours.
• Influencing Roles: These are roles where you don't have people reporting to you, but instead your primary objective is to influence people around you to get things done. A typical such role is that of an internal consultant in a company.

I think both roles have their unique challenges, but I believe that the latter is just a little bit more difficult, because people easily understand hierarchies and reporting structures whereas they don't often want to take instructions from people at their own level. I cannot think of many roles that fall outside the above two categories. In fact, even team management is a form of inflencing and thus the first category may be a subset of the second. Are we to conclude that there is nothing else to management apart from influencing? If that is so, it is rather unfortunate that most b-schools (at least the Indian ones) don't have many courses on influencing.