Both buildings are situated in City Hall, Algonquin: a skyscraper and Liberty City's city hall. This has caused confusion as to which building is actually known as the Civic Citadel, and it is likely that the name was used liberally by the developer without consideration of consistency.
As city hall
During "Entourage", the player is instructed to drive Bobby Jefferson to the "Civic Citadel", which is revealed to be Liberty City's city hall (being based close to scale on the real-life New York City Hall building). This is the only instance where the building is referred as such.
As a skyscraper
The Civic Citadel name is also used to refer to a skyscraper further south from city hall, clearly based off Woolworth Building in New York City. While the building's entrances reveal it could be known as the Woodworld Building, hard copy maps reveal that a "Civic Citadel" is located on the very spot of the building, on a block bordered by Diamond Street, Calcium Street, Union Drive West and Liberty Lane.