I believe that "Starting Current" is simply a term that we give to the value of current a motor will draw when energized at rated voltage but the rotor is not turning. Thus, the instant an idle motor is energized, it will draw starting current, but as the motor rapidly comes up to speed, the current draw rapidly deminishes to normal run current.
The magnitude of the value of a motor's starting current should not change regardless of connected load. What does change is the duration time, how long the motor takes to spin up to normal speed. I've seen motors driving large fans that take so long to come up to speed (several seconds) that the overloads trip.
Starting a motor under full load increases the time the motor will need to come up to speed. This excess startup time can possibly overheat the motor if done repeatedly. So, centrifugal pump motors are frequestly started with a shut-off head to help aleviate this (not moving water = minimal load).
Hope this helps some,