As used in this act:

  (a) “State agency” means a department, board, commission, office, agency, authority, or other unit of state government. State agency includes a state institution of higher education.

  (b) “Unit of local government” means a political subdivision of this state, including school districts, community college districts, intermediate school districts, public school academies, cities, villages, townships, counties, and authorities, if the political subdivision has as its primary purpose the providing of local governmental service for citizens in a geographically limited area of the state and has the power to act primarily on behalf of that area.