Sync speed is the fastest shutter speed you can use with flash, period.
Marketing departments like to push the "FP" trick flash modes that seem to let you sync at any speed, even 1/8,000. This doesn't count as far as I explain later here. Canon calls this "High Speed Sync" and I forget what Sigma and others call it. It is not a substitute for genuine fast sync speeds.
Since only a fraction of the light at any time is exposing the film or CCD you lose a lot of light, again getting you back to the problems of limited flash range. The loss of light also depends on the shutter speed you use, thus the flash guide number used in manual calculations in 1.) above changes with shutter speed! You lose most of the light at the faster speeds and lose less at slower speeds.