You are correct. Most people haven't looked at a London map too closely, so there is a limited understanding of what the City of London is.
> The City of London, London's ancient core and financial centre − an area of just 1.12 square miles (2.9 km2) and colloquially known as the Square Mile − retains boundaries that closely follow its medieval limits.
Greater London, in total, is larger than Los Angeles.
> The City of London, London's ancient core and financial centre − an area of just 1.12 square miles (2.9 km2) and colloquially known as the Square Mile − retains boundaries that closely follow its medieval limits.
Greater London, in total, is larger than Los Angeles.
https://mapfight.xyz/map/los.angeles/#london
https://www.londoninfoguide.com/how-big-is-london-uk.html
The congestion charge is not for Greater London and the Manhattan toll is not for all of Manhattan.