Thomas, I agree that the structure of your organization as per your description is a functional one. The fact that there are few people in the organization illustrates that there is no need for complex organizational structures that may not be feasible or applicable to your situation. A functional structure is ideal considering that your work environment is stable in that you have a defined region within which you operate with your supervisor. In addition, since you and the supervisor do similar work it is prudent to assume that your job unit is specialized making a functional structures the best option for your organization. Another attribute of a functional organizational structure according to is the reporting or organizational hierarchy system where you report to the supervisor and he reports in turn to his immediate boss. This system creates a functional hierarchical organization structure with a clearly defined chain of command.
However, your career field organization has an entirely different organizational structure considering that it combines both functional and flat organizational structure to create a hybrid matrix structure. Considering that the organization being described is military, the matrix grid structure is ideal since to distribute authority to different management centers where the different unit or team leaders report to single commander. Their matrix grid structure ensures that each unit is able to discharge its duties and responsibilities towards the attainment of a set goals. These could be coordinated to ensure that the different outcomes of each unit are combined to result in a single major outcome. Evidently, the organizational structure depends on the size, functions and goals of the various units within the organization.