What is the difference between academic and administrative department heads? In a comment, it was quoted that some universities have administrative or academic department head. I sensed this difference before (but do not remember specifically), but I always thought that the latter is the case: one of the faculty members of a department is appointed as the head or hiring a new faculty member to serve as the department head (or vice versa in some sense).

How and why are administrative and academic heads different?
An administrative head of department heads up the administration of the department, and will typically have little or no involvement in the direction or the content of the research or teaching.

An academic department head leads the academic direction of the department. This often include somes administrative duties. Well, they nominally lead the academic direction of the department. In theory, they guide the direction of the department's researchers and teaching. In practice, that's like herding cats.