A license fee is hereby imposed for the privilege of operating upon the public highways in this state any vehicle of a type which is subject to registration under the Vehicle Code, or any trailer coach which is required to be moved under permit as authorized in Section 35790 of the Vehicle Code and which is not subject to local property taxation pursuant to Part 13 (commencing with Section 5800) of Division 1. Vehicles of banks, including national banking associations, shall be subject to all provisions of the Vehicle Code to the same extent and same manner as other vehicles, and shall be subject to this part.