Yup, sounds like management to me.
That's a joke because it has a kernel of truth. As you say it is a specific skill set to manage people. The traditional corporate (and public organisation) hierarchy works on the assumption that being good at what you do also means you can manage the people who do what you do. My professor at uni in Organisation and Management referred to the field as the rantings of dead bearded white men. Then he played us some Rage Against the Machine.
It also impacts pay scales in odd ways. Like our local public health organisation had to raise the salary of the chief officer because the organisation wanted to hire a medical doctor specialist and had to offer a fair bit over "market price". As they uncritically put it "our highest officer has to have the highest salary". No one ever asked the question, "why?". More properly one should consider how taxing is the position and what are the requirements for it. When I was at uni flat hierarchys were all the rage but I've not seen one successfully implemented yet.