Government probably means the Central or Federal Government which controls the whole country. They usually undertake the important functions of national interest such as the Police, Defence, Health and Eduction.Government Technical College(GTC)
State Agricultural Institute (SAI)
State probably means the government of a state or province in a country which is given the power by Federal Government to govern and adminster a particular state.
The difference is not clear-cut though and the terms are used interchangeably. Government may mean the State Government and State may refer to the government of the country as a whole.
not a teacher