Structural and frictional properties of single-layer and bilayer graphene films on a SiC(0001) substrate are studied by means of atomic force microscopy with atomic resolution. Friction on single-layer graphene is found to be a factor of two larger than on bilayer films for a variety of experimental situations. The friction contrast is found not to originate in differences in structural properties, in lateral contact stiffness, or in contact potential. The transition from atomic stick-slip friction to a regime of ultralow friction is found to occur at normal loads of 40 nN when the tip-sample interaction potential approaches 0.1-0.2 eV.