What is the difference between transresistance and differential resistance?
Transresistance, as given by the definition, refers to an input current and an output voltage. Thus the current and voltage are not meassured at the same points.  For example, the transresistance of an amplifier is the ratio of the change in output voltage of the amplifier to the input current of the amplifier.  Differential resistance, on other other hand, refers to a current and a voltage measured at the same points.  It is usually used to describe the behavior of a non-linear resistor. A linear resistor exhibits the same resistance (ratio of voltage across it to current through it) independent of the actual magnitudes of the voltage and current (at least up to its power limits).  A non-linear resistor will have a varying resistance depending on the magnitude of the current through it.  The differential resistance of such a device is the ratio of a small change in voltage to the resulting change in current measured at some fixed voltage level. It will change as the fixed voltage level is varied, which is why the resistor is designated as non-linear. At any rate, the difference in the two terms is the points where the voltage and current are measured: different points for transresistance (which is what the "trans" refers to) and at the same points for differential resistance.