I recently had someone tell me that the time it takes for both curtains of a focal plane shutter to complete their travel doesn't change appreciably beyond the maximum flash sync speed. In other words, shutter speeds of a focal plane shutter are just measures of how long the travel of the 2nd curtain is delayed once the first curtain begins its travel, but the total time the curtains are in transit is never appreciably longer than the x-sync speed. For example, if setting the shutter speed to 1/8000, the curtains will be in transit for 1/250 of actual time, since that is the fastest the mechanism can physically propel the curtain.
Kinda. It is true that focal plane shutters are also called 2 curtain shutters. The first current opens and the 2nd one follows to close. In modern cameras they travel vertically. At slow shutter speeds, the 1st current fully opens prior to the 2nd curtain firing. At increasing shutter speeds the 2nd curtain fires prior to the 1st curtain being fully opened such that an open slit moves across the sensor plane. Faster shutter speeds mean a narrower slit.
What is somewhat lost in these discussions is the timing piece. The highest flash sync speed is the fastest speeds the shutter supports such that the 1st curtain remains fully open prior to the 2nd curtain firing AND the system electronics, including the flash head, can predict and input a flash pulse into the event in between the 1st curtain getting fully open and 2nd starting it's travel to close (shutter fully open). This part is not trivial!
While there is such a thing as high speed flash, what DSLRs and associated flash heads offer is mode in which the flash head pulses at very high rates, but at lower power, such that to a focal plane shutter slit, it looks like continuous light. Nikon calls this Auto FP mode.
Most geometric distortion images used as examples were from a time when focal plane shutter moved at a glacial pace compared to normal movement.