As the name says, the FBI Washington has the same body design as a Washington.
In GTA Vice City, the car isn't used by the FBI as the FBI Rancher serves as their main vehicle. Even though the car isn't used by the FBI, the car can be found behind the music store close to the pizza shop in Downtown, Vice City. The car features a charcoal paintjob and side triming, make the car distinguishible in traffic and from a regular Washington. The car emits a siren but no strobe light. The player can also use the car in Vigilante side-missions.
In GTA Vice City Stories, the car is used by the FBI replacing the FBI Rancher. When the player recieves a 5-star wanted level, the car will appear with a black color. The FBI Washington's that are used in road blocks appear to have a white paintjob. The car also features a red flashing strobe light emiting from the dashboard, allowing the player ofr FBI to clear traffic on the road.