I don't see a discrepancy in the wiki and I am not absolutely sure where you see one.

A building=fire_station is a building that was constructed to be used by fire fighters during their work. If that is the case the building=yes should be replaced on these two buildings:
https://www.openstreetmap.org/way/761383268
https://www.openstreetmap.org/way/1314771464

An amenity=fire_station is the area used by the fire fighters to park trucks, do office work, repair equipment and so on. In some cases that is only one building but in other cases that includes outside area too. That seems to be the case here.

I do not think that any building here is named "Muttaburra Rural Fire Brigade". As I do not know this place I could be wrong. But probably only the fire station is named like this. In most cases the buildings wont have any name. Even if the sign with "Muttaburra Rural Fire Brigade" is attatched to a building wall that building is probably still unnamed. If you have a name plate with "GeeMaps!" on your t-shirt in real life than that is still your name and not the name of your t-shirt. The buildings could be tagged operator="name of fire station"

For me the wiki pages make sense. Did you understand why I think this? If not, can you try again to tell me what exactly is not fitting together? Maybe there is something I am just not smart enough to see on my own.

And independently from all these questions about buildings: I still do not see why there should be an area and a way with the same taggs.