what happens when both anode and cathode voltages are same for a diode?
This is actually a good question, and should not have been downvoted. The answer is that it could be any (forward) current (including zero)- you cannot tell what the current is from the voltage. Same as with the ideal wires we draw on a schematic. That is a consequence of the 'ideal' assumption- it's not a physical reality.

If you are trying to analyze a circuit with ideal diodes you have to treat them sort of like wires that are there if the voltage drop across them would be in the correct direction if they were removed.

The only time this comes up in reality is with a superconducting wire- if there is zero volts (exactly zero volts, not too low to measure) then there could be +/- any current through the wire (up to some limit in reality).