Is surge current the same as short circuit current?

Not usually, but it may depend on the context. For instance, surge current might be used for a generator that is going to start a motor. Motors draw high current as they start, then the current drops to a normal level, called RLA, or running load amps. Generators have a watt rating for continuous operation called running watts, but they also have a 'surge' rating. You might see a generator listed as a '6000/5200 watt. The 6000 watts is the 'surge' rating. This means the generator can supply 6000 watts for a few seconds, such as might be needed to start a motor, but cannot supply more than 5200 watts continuously. Short circuit current on the other hand simply means how many amps will flow instantaneously if you drop a wrench across the two wires! For a normal utility power service, the short circuit current, also called fault current, can be several tens of thousands of amps, even though the main breaker is only a couple hundred amps.