Right. Indonesia is divided into provinces (provinsi). Provinces are made up of regencies (kabupaten) and cities (kota). Regencies and cities are divided into districts (kecamatan). Districts are divided into urban communities (kelurahan) or villages (desa).
Both regency and city are at the same level, having their own local government and legislative body. The difference between a regency and a city lies in differing demographics, size and economics.