The logical relationship between two previously defined "memory resistors" is revealed by constructing and experimentally demonstrating a three-terminal memistor equivalent circuit using two two-terminal memristors. A technique is then presented, using nanoimprint lithography in combination with angle evaporation, to fabricate a single nanoscale device with a footprint of 4F(2), where F is the minimum lithographic feature size, that can be operated as either a two-terminal lateral memristor or a three-terminal memistor inside a crossbar structure. These devices exhibit repeatable bipolar nonvolatile switching behavior with up to 10(3) ON/OFF conductance ratios, as well as the desired three-terminal behavior.