Philadelphia is a "City of the First Class" due to PA law regarding the organization of townships and cities within the Commonwealth. This is designated by the state if and when a township or city would like to change its status or form of government (ie: township to city) or change its class (ie: City of the Fourth Class to Third Class). The designation may be changed after a certain amount of censuses are done by the US government and that township or city applies to the state to have the change according to the census data with regards to population.
http://www.lgc.state.pa.us/deskbook06/Basics05_Municipalities_How_They_Change.pdf
Pittsburgh is NOT a City of the First Class. It is a City of the Second Class.
Cities in PA have 4 classes.
Townships have 2 Classes.
Boroughs are not classified as classes.
I hope this forever answers that question.