Voltage during LED ON and OFF
But when it is not glowing, why is there a voltage difference between the anode and cathode?


This reminds me of "If a tree falls in a forest and no one is around to hear it, does it make a sound?" In your case it would be re-written as "if noone is measuring the voltage will there be a voltage drop?"







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The equivalent circuit.

Your meter has an impedance and will pass some current while taking the measurement. This current flow will cause a voltage drop.



Figure 2. I-V curves for typical LEDs. Source: LEDnique.

Your measurements indicate a 1.3 V drop. You can see from Figure 2 that all of the visible LEDs will pass tiny currents at that voltage.