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?
However it is generally only those local government areas which have been specifically granted city status
And how are city status granted?
Usually on the basis of population that entitles to refer to themselves as cities
And what have to be the population to be granted the city status?
the City of ______" or similar.
Some of the urban areas of Australia are governed mostly by a single entity (see Brisbane and other Queensland cities), while others may be controlled by a multitude of much smaller city councils. Also some significant urban areas can be under the jurisdiction of otherwise rural local governments. Periodic re-alignments of boundaries attempt to rationalize these situations and adjust the deployment of assets and resources.
Ireland.
The 2001 Local Government Act restyled the five county
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