The friction between two model atomic force microscope tips and two hydrocarbon monolayers has been examined using molecular dynamics simulations. An amorphous hydrocarbon tip and a flat diamond tip were both employed. One monolayer was composed of linear alkane chains and the other was composed of chains that were polymerized in a regular pattern near the tip-monolayer interface. When friction is decomposed into the forces on individual chains pushing and resisting sliding, the monolayer composed of linear alkane chains exhibited strong pushing forces immediately after clearing tip features at the sliding interface. When this monolayer is paired with the amorphous tip, the strong pushing forces resulted in low friction compared to a monolayer composed of polymerized chains. When the diamond tip is employed, commensurate meshing with the chains of the linear-alkane monolayer resulted in chains resisting tip motion for longer durations. The consequence of this is higher friction compared to the polymerized monolayer, despite the linear-alkane monolayer's more symmetric chain response at resisting-to-pushing transitions.