One is the local government area for the City of Sydney, the other is the boundary for the city of Sydney. When you say Sydney, most people assume you mean the latter, unless you explicitly say the LGA of Sydney or “City of Sydney”.
There are three Sydneys, a CBD area just South of the Harbour Bridge, name Sydney, admin_level 10, a larger area which covers the smaller Sydney boundary. This is the Council of the City of Sydney (short name Sydney), admin_level=6 then the largest area of all extending almost to the Blue Mountains. Its name is also Sydney with admin_level=7.
I did not know until recently when I obtained confusing results from a query. After some trouble, I discovered that there were more than one Sydneys.