(a) Township supervisors, township clerks, and township collectors shall be elected in their respective townships in Cook County at the time of the regular township election provided in the general election law. They shall hold their offices for 4 years and until their successors are elected and qualified.
     (b) Those townships in Cook County lying outside the corporate limits of the City of Chicago, the boundaries of which are co-extensive with the corporate limits of a city, village, or incorporated town, shall elect a township assessor at the time of the regular township election provided in the general election law. Those township assessors shall hold their offices for 4 years and until their successors are elected and qualified.