As used in this act, unless a different meaning clearly appears from the context:

  (a) The term “public corporation” shall be construed to mean any county, city, village, township or metropolitan district, of the state of Michigan, or any authority created by or pursuant to an act of the legislature.

  (b) The term “governing body” shall be construed to mean, in the case of a county, the board of supervisors; in the case of a city, the council, common council, commission or other body having legislative powers; in the case of a village, the council, common council, commission, board of trustees or other body having legislative powers; in the case of a township, the township board; in the case of a metropolitan district, the legislative body of the district; and in the case of an authority, the body in which is lodged general governing powers.