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There is Star City and Starling City but I've heard the Flash's home referred to as Central City and I know it shouldn't be this confusing but it is. Are Star City and Central City the same city?
They are two different places. Indeed, the Flash is sometimes shown travelling betwen them.
Star City (previously called Starling City) is the home of the Green Arrow.
Central City is, and always has been the origin city of The Flash in the TV Show and the DC Comics
In the Arrowverse (TV series) it is (Green) Arrow's hometown that starts out as Starling City, and then becomes Star City in the forth season.
Whereas Central City has long been the hometown of the Flash.