Question:

We have adopted that "the army, internal security, industry, and international relations" are independent departments and not sectors, so why do we use the word ‘sector' and not ‘department'? May Allah reward you.

Answer:

Yes, each one of them is an independent department, but it is an administrative department that may be named as such, however it is not related to the department of people's affairs rather it is an independent department.

Refer to the chapter: "Bayt al-Mal" State Treasury (p. 135 Arabic ed. / p. 129 English ed.  The Institutions of State in the Khilafah "Caliphate"), it states the following:

"We have already adopted that the wali is given a special authority that excludes the army, judiciary and funds. Thus, the whole army will be a central department (presided over by Amir al-Jihad). The judiciary will be a central department (known as judiciary), and the entire funds form a central department (known as bayt al-mal), which is separate from any other organisation in the State, and follows the Khalifah as do the other organisations."

As you can see, it is called department even though it is an administrative section. However it is a centralized department i.e. not affiliated with the Administration department (people's affairs).  Likewise, "the whole army will be a central department (presided over by Amir al-Jihad)," "The judiciary will be a central department," and "funds form a central department (known as bayt al-mal)."

Therefore each department whose work includes administration is called a department, and if there is the fear of confusion which department is considered from the departments, it is possible to add the word ‘central'. If there is no fear of confusion, then department is appropriate, and it is clear that the army, internal security, industry, and international relations are not confused with the administrative department (People's Affairs) in which each department is called a department.