Is there any relation between charging rate and discharging rate? Sometimes when I do not use the  original charger but a different one it would take less time to fully charge the device than the original charger would do. But I can feel that discharging rate is higher after using these chargers. 

Is it true?  If it is true, then what is the actual reason?
I think not. faster charger actually put more energy into your battery (1A = 1W * 1V^-1). your battery's Voltage is at charging and discharging the same (or to be specific, it's rising while charging and dropping while discharging, but the same amount *), so basically the difference between the two chargers is the energy (A) which comes, and because of the same Voltage (V) the Power (W) must be different. if you discharge, the processor (and display,...) consumpts power (W), but the Voltage is still the same.

* what is not the same is how fast your battery would discharge in relation to the actual charging percentage (or, better known as slower charging at end of charging)