Mark - as Phil says, the actual flash duration is much less than 1/200.
The reason you use a max speed or between 1/160 and 1/250 (depending on exact camera and triggers), is that for flash to work the camera shutter must be fully open at the instant the flash fires.
A camera shutter is actually 2 shutters - you start with 1 open and one closed.
When you trigger the camera, the first shutter opens, then after required exposure duration the second one closes.
But the shutter actually takes a bit of time to open (and close).
So if the shutter takes 1/230s (for example) to fully open, then if you had a shutter speed of 1/250, the second shutter is actually already closing before the first shutter has fully opened.
By setting the max shutter to 1/200, there is time for the 1st shutter to open, then the flash to fire, then the 2nd shutter to start closing - but since the flash is much brighter than the ambient light, you just see the scene as illuminated for that brief instant of the flash, and the additional exposure from the ambient light vanishes to black.