Well a station is simply just an individual fire station.
A department is the whole department wether its one station or twenty stations.
A battalion is usually a group of stations within the same department that are assigned to a battallion chief for example (station 1, 3, 5 are assigned to battalion chief 1 and stations 2, 4, 6 are assined to battalion chief 2)
A brigade I am not real familiar with but the brigades that are in my area usually consist of firefighters working at an industrial location such as a wearhouse or powerplant ( like where I am from they have the omaha public power plant fire brigade) These guys fight fire in the plant and do not have any trucks they only have an exsisting water source and hose. They also have the local volunteer department come in with trucks to assist.
Only thing I can add to that is the term "Brigade" is similar to a Fire Department in the UK/Commonwealth nations (England, Australia, etc). A Battalion is usually made up of a combinaiton of Engine and Truck Companies and is assigned a specific geagraphical area within the jurisdiction.
Jessica,
First the only stupid question is the one you don't ask.
Second after 30 years I didn't know what a wagon or squad was. Here in Delaware we only have engines and rescues.
Third a Brigade is at least in America is an industrial department made up of workers. In New Castle County Delaware they all have the same number , Dupont, Valero Oil, Ciba Giegy all have number 35. Only the Hospital has a different number, 38, which I really don't understand. None of them respond outside of thier area.
You remind of my son with the geat questions...except you're white a girl and pretty.