I suspect your usage of the term is much more common in India (and possibly other nations outside the US).

I'm really curious as to whether this difference in interpretation is just a linguistic fluke, or if it actually reflects some larger cultural difference in how we in the US view our government compared to how people in India and Spain view theirs.

Do you have a different word which encompasses all governmental bodies and organizations? The State, perhaps? Or would you not consider the courts to be part of the State either? Obviously the courts are involved in governing, since they interpret the law and they have legal authority granted by the constitution. How then are they not part of the government?