What is the difference between short circuit making current and short circuit breaking current of switch-gears?
Is short circuit making current and short circuit making capacity same?

Short circuit making current is the actual current that would flow if you shorted the energized conductor to ground. This is determined by the voltage driving the circuit and the circuits total impedance. The short circuit capacity is the maximum amount of short circuit current that the switchgear is able to safely and mechanically interrupt without failing or blowing up. Hope this helps.

Short circuit making current should be the high current which would flow if you switch on a circuit with a fault in it

Short circuit making current should be more severe than SC breaking current. But in both cases transients takes place.