departemento

The French sense leads, and that is not an accident. English department is a wide word: a shop has one, a university has one, a government has one. In Esperanto departemento is narrower and more concrete, and it means primarily the administrative division of a country that France invented in 1790 and exported: a departemento has a prefect, a capital and a number. If you are translating a French address, a French news item or a French novel, this is your word. Almost anywhere else, it is not.

Two fences, and you need both. Fako is the department in the sense of a field or a section of an organisation: the history department, the toy department, the compartment in a bag. That is what English usually means. Sekcio is a section or subdivision of a body, the piece you get when you cut something up on paper. Neither is a place on a map. A departemento is.

And the map ladder. From the top down: ŝtato, then regiono or provinco, then departemento, then distrikto, then komunumo. The boundaries between these are political rather than linguistic, and every country carves them differently, which is why Esperanto keeps them all rather than picking one. Use the word the country itself uses, and the reader will know which system you are in.