As such, it is simultaneously a city, which is a municipal entity, and a county, which is an administrative division of a prefecture.
This is because the counties that county-level cities have replaced are themselves large administrative units containing towns, villages and farmland.
While the idea of a "city" being a unit consisting of several "towns" is not a common one in English-speaking world, a somewhat similar naming convention is used for local government areas in some parts of Australia.
For example, in New South Wales such a unit may often be called a "city" (rather than a traditional "shire"), and consist of "towns".
E.g. City of Blue Mountains is made of a number of towns (Katoomba, Springwood, etc.).