It's because a diode is not a resistor. When current passes through a diode, it causes a voltage drop across it and a multimeter shows that as the equivalent resistance. But the equivalent resistance is highly non-linear, which means that the voltage drop is not proportional to the current. Conversely, the current is not proportional to the voltage.
For example, a diode may have a voltage drop of 0.6V when you pass a current of 1mA through it. That is seen by a meter as a resistance of 600 ohms. If you pass 2mA through a 600-ohm resistor, the voltage drop will be 1.2V. But if you pass 2mA through the same diode as before, the voltage drop may be only 0.62V, and it will be seen by the meter as a 310-ohm resistor.
A multimeter, whether digital or analog, puts out different currents at different resistance ranges. Since the diode does not behave like a linear resistor, the meter shows different equivalent resistances for the same diode.