However, I'm confused why resistance mode has five different "modes"(2M, 200k, 20k, 2k and 200 ohm) while diode mode does not.
The voltage drop for diodes will not come in as wide arange as resistors.
.6-.7V for Silicon diodes, a bit less for Germanium or Schottky diodes.
LEDs will range from a bit under 2V to over 3V.
Many multimeters will not be able to turn on LEDs, some only red LEDs and some all.
Zenerdiodes come with many reverse voltage drops.
The diodemode on a multimeter is usually just for the simple diodes in rectifiers, logic, etc. to tell you if the diode is good or not.
For testing LEDs and Zeners you can better use different equipment where you can choose higher voltages and different currents.
Also, how does the DMM know, that now it is in the 2k resistance test mode and not in diode test mode when the switch position is the same. Or is the amount of current sent out by the DMM the same both in 2k resistance test mode and in diode test mode?
With this meter there is only one mode under this switch position.
The 2k resistance mode IS the diode mode.
Other meters may have a separate diode mode (under a different switch position or shifted) that will behave different.
If you want to get to know your multimeter better you should get a second one.
Connect them together to measure eachother:
How much current produces the resistance or diode mode?
How much voltage produces the resistance or diode mode when there is only the high resistance of the other meter conencted?
What is the resiatnce of a meter in voltage mode?
And what is the resistance between the common and current jacks?