Semi-government is a term which is usually used to define a company, department, or an institute which is basically a government run institution however it enjoys a certain degree of independence.Mostly those institutes are defined as semi government institutes that are not run directly by the government but a department which is under the control of government.
For example, If armed forces of a country run a educational institute, the educational institute follow the rules of armed forces. However the armed forces are controlled by the government, so the educational institute will be labelled as a semi government institute.