You are correct that sector is the answer most fitting.
Section = a part of a whole, sometimes made physically separate (or conceptually separate) without great thought or reason - or with a system such as a grid, rather than through consideration of separate functions.
Sector = a part set aside for a specific purpose or function (this is what you are referring too.) A sector may or may not be in a grid system, but if it is, gridded sectors may have unique functions. A sector can have physical boundaries or it can be conceptually set apart.
Conceptually separate: Within the whole, there are those that work with a specific, separate element of the business.
area = a space or conceptual space, being thought of as separate (not necessarily set apart in any literal, physical way)
Physical area examples: section of a building or land
Conceptual areas: business type or education category
Part = a piece of a larger whole: the term does not specify importance to the whole. Some parts are quite important while some are less important. Every section, piece and sector can be thought of as a part.
An area is not a part. Parts can be thought of both separate yet connectable. Areas tend not to be separated physically.