Private owner-operator or owned by government?

Only IETT is government company. This one and all others under ÖHO are private companies (bus owners). But they all work in one unified system coordinated by IETT.

Do drivers own the bus itself?! Because in Tehran most drivers are owners as well.

No, buses are owned by companies. Driver himself cannot afford such bus and permits for bus routes are not issued to private persons. But if it is a dolmus/minibus then driver most probably is an owner of it and has his own license to operate.