Greater London consists of many boroughs or 'cities', way more than three. Each is its own municipality, just like Westminster.
The City of London happens to be one of the smallest, and least populous.
Edit - on rereading this, I realise you may have been referring to the fact that Westminister has 'City' in its name, whereas most others boroughs use the word 'Borough'. I'm not aware of other boroughs in Greater London that are also 'Cities' in that respect.
I'm not aware of any other London boroughs other than Westminster that actually hold the City status though. Being both a borough and a city is pretty unique I think.
Also interesting, those people live only within 4 electoral wards, whereas there are 25 total electoral wards within the City.
Within the remaining 21 electoral wards, votes are controlled by businesses (mostly banks and the like), and the amount of votes that each business receives depends on it's size.
The City of London happens to be one of the smallest, and least populous.
Edit - on rereading this, I realise you may have been referring to the fact that Westminister has 'City' in its name, whereas most others boroughs use the word 'Borough'. I'm not aware of other boroughs in Greater London that are also 'Cities' in that respect.