Think that's a sensible approach (to looking at things) but there's a difference between how you work together with someone that you and your coworkers have decided are good at coordinating work, and a traditional boss. The coordinator is working for you, not the other way around, if that makes sense? Like the difference between having an elected president and a dictator.
This is correct. Coordinators do serve some of the same functions as a manager, but the difference is they are appointed by the people they are managing. We call this "dynamic hierarchies by consent". Coordination also rotates, and many members have been in the role and then moved on from it.