A city council is a town council 
And what is a town council?
They are like local government
And are they elected or designated by someone?
City council
A city council, town council, town board, or board of aldermen is the legislative body that governs a city, town, municipality, or local government area.
Australia.
Because of the differences in legislation between the states, the exact definition of a city council varies. However, it is generally only those local government areas which have been specifically granted city status (usually on a basis of population) that are entitled to refer to themselves as cities. The official title is "Corporation of
Parish councils in England
A parish council is a civil local authority found in England and is the first tier of local government. They are elected corporate bodies, have variable tax raising powers, and are responsible for areas known as civil parishes, serving in total 16 million people. A parish council serving a town may be called a town council, and a parish council serving a city is styled a city council; these bodies have the same powers, duties and status as a parish council.
Civil parish councils were