An electronic flash has a 'rise time' as well as a 'duration'. During the rise time, the output is increasing to its peak, and the 'duration' is the time interval during which the shutter needs to be fully open in order to capture the output of light. For speedlights, they generally have a fast rise time and fast output duration, as they generally are limited in total output. Studio flash units, typically being more powerful than speedlights, have somewhat slower rise times and long durations in order to output all the light. Think of fire hoses...it takes a bit of time to open the valve fully and for the max output to be achieved.
So a fast shutter speed like 1/250 works with a speedlight or most of the lower power studio flash units, while the slower shutter speed is needed for really powerful studio flash units. (note: Some studio flash unit designs do not follow the generality about longest duration = max power output.)