The voltage being applied to this relay in the socket is around 2.4V and the relay is not switching. But I got another unit of the same relay and it worked. Is the first relay damaged or is it due to something else?
Also, what is minimum release voltage? In this case it is 0.3 V, so what is minimum voltage I should apply to the relay to make it switch?
The datasheet linked above has the figures you quoted for a relay with a Rated Voltage of 6V.
Rated Voltage - 6V
Max Operating Voltage - 4.5V
Min Release Voltage - 0.3V
Max Applied Voltage - 7.8V
What do these all mean?
Rated Voltage 6V - this is the nominal operating voltage - the relay should operate from a voltage reasonably close to this. But power sources are rarely precise, so we need to know more information...
Max Operating Voltage - 4.5V. The relay is guaranteed to operate (switch on) at Max Operate Voltage (4.5V) or higher, so you really can't expect it to switch at 2.4V. If one does, either it is performing better than spec, or check its coil resistance to see if it's a mis-labelled 4.5V relay!
Min Release Voltage - 0.3V When you want it to switch off, reduce the voltage below Min Release Voltage - it will probably release at higher voltages but don't rely on it.
Max Applied Voltage - 7.8V Above this voltage, the coil may overheat and fail. So just keep the voltage less than Max Applied Voltage (7.8V)