the City vs City of London

the City and City of London both are nouns.

Word	Noun	Adjective	Verb	Adverb
the City	Yes	No	No	No
City of London	Yes	No	No	No

As nouns, the City and City of London are synonyms defined as:

the City and City of London: the part of London situated within the ancient boundaries; the commercial and financial center of London

the City (noun)	City of London (noun)
used to allude to the securities industry of Great Britain	the part of London situated within the ancient boundaries; the commercial and financial center of London
the part of London situated within the ancient boundaries; the commercial and financial center of London