We use atomic force microscopy (AFM) to determine the frictional properties of nanoscale single-asperity contacts involving octadecyltrichlorosilane (OTS) monolayers and silicon. Quantitative AFM measurements in the wearless regime are performed using both uncoated and OTS-coated silicon AFM tips in contact with both uncoated and OTS-coated silicon surfaces, providing four pairs of either self-mated or unmated interfaces. Striking differences in the frictional responses of the four pairs of interfaces are found. First, lower friction occurs with OTS present on either the tip or substrate, and friction is yet lower when OTS is present on both. Second, the shape of the friction versus load plot strongly depends on whether the substrate is coated with OTS, regardless of whether the tip is coated. Uncoated substrates exhibit the common sublinear dependence, consistent with friction being directly proportional to the area of contact. However, coated substrates exhibit an unusual superlinear dependence. These results can be explained qualitatively by invoking molecular plowing as a significant contribution to the frictional behavior of OTS. Direct in situ comparison of two intrinsic OTS structural phases on the substrate is also performed. We observe frictional contrast for different local molecular packing densities of the otherwise identical molecules. The phase with lower packing density exhibits higher friction, in agreement with related previous work, but decisively observed here in single, continuous images involving the same molecules. Lateral stiffness measurements show no distinction between the two OTS structural phases, demonstrating that the difference in friction is not due to divergent stiffnesses of the two phases. Therefore, the packing density directly affects the interface's intrinsic resistance to friction, that is, the interfacial shear strength.