I disagree with Sid, his model is a two tier management model, where your either management or your not. There nothing wrong with that model and you do see it often enough.
According to Sid though a school wide "librarian" who supervises 3 campus librarians, 3 additional campus assistant librarians, 6 pages/clerks, a small staff of IT support personal as well as his/her own assistant, in addition to managing a substantial budget doesnt qualify as an "administrator". I would disagree.
What it really comes down to is what does the person do, and what responsibilities are they given by senior admin. A counselor whos job description is mostly student management, regardless of title is in an administrative position. If the schools behavior management policy delegates that a student referred for behavioral action first stops off at the counselors office, and that counselor determines wether the students situation warrants further corrective action or gets sent back to the classroom, thats administration.
In a number of cases counselors/librarians have administrative functions because they have administrative tasks, in some cases for no other reason then these individuals have the time and resources to do them.
Again, in a small school without a SEN/LS HOD, the counselor may supervise and manage SEN/LS services, and in such case is functioning as the SPED HOD. That makes them an admin, if only a junior admin.
Under Sids description an AP/VP/DP/Dean who doesnt hire or fire wouldnt be considered an admin? I know lots of APs/VPs/DPs/Deans who would disagree with that, mainly because its just wrong.
If we look at an ISs admin team you can describe 4 tiers of administration based on their general level of Authority:
1) Executive Admin: Often the HOS the school Director these individuals exercise "hiring authority" meaning they can push the button (too hire) and pull the trigger (to fire). They run the school as ownerships representative. In an American school district this would be the superintendent.
2) Senior Admin: These are the principals (but coordinator is used sometimes) and assistant principals (AP's), Vice Principals (VPs), DP's (Deputy Principals) and Deans. A school usually has a principal per 'school', such as the primary and secondary school principals (or intermediate/middle school principal) or in the case of IB PYP, MYP, DIP school principals. These admin have "tasking authority", meaning that they can direct what you do. Your going to teach these classes at these times, and your there is a faculty meeting at 4:00 on friday, attendance is mandatory, etc. In some school the senior admin mainly principals may also have executive (hiring/firing) authority.
3) Junior Admin: These are the HODs (Head of Department) and Coordinators. these individuals have "reporting authority" meaning they can and do report on your performance and actions from a variety of sources including observation, written evaluations and informal verbal commentary from other parties.
4) Professional Staff: These are the counselors, librarians and other non supervisory coordinators who have documentary authority. They produce documents that may reflect aspects of your service and performance. A DIP coordinator that compiles a report on exam scores correlated to classroom marks could use all sorts of metrics to reflect your performance in a positive or negative light.
I really need to address the title of coordinator, which in IB is even more confusing, since a coordinator could have varying degrees of authority. Coordinator could describe anyone from a principal to professional staff.