A bit more detail:
Focal plane shutters must be limited to (typically) about 1/200 second shutter speed to be able to sync with flash. Some camera shutters are a bit faster, some are a bit slower. The camera specs have this Maximum Sync Speed spec, typically about 1/200 second shutter. If the camera can detect a flash is present, the shutter speed will not be allowed to go any faster, because results would be bad. https://www.scantips.com/lights/flashbasics2c.html shows why this limit.
Which is no problem, because camera flashes are called speedlights because the flash is extremely fast (very short duration). They are not so fast at maximum power level, but extremely fast at low power levels. Varies a little with brand and model, but perhaps 1/10000 second at 1/16 power, perhaps 1/30000 second at 1/64 power (Nikon SB-800 flash).
For water drops, using perhaps 1/64 flash power at about 2 feet at f/16 and ISO 400 will stop any water drop splashes (using 1/200 second shutter, which is not a factor, except fast as possible to sync, to keep out any ambient light). See https://www.scantips.com/speed.html for the idea. Works for hummingbird wings too, and in some cases, can stop bullets in flight.
The flash stops the motion, the shutter merely has to be open to pass the flash.
Strong continuous ambient light (like bright sunlight) can still illuminate and show blur on the motion, but in a halfway dim room (really, any normal indoor lighting), the same 1/200 f/16 exposure without the flash will be a very black picture, with no effect. The very short flash duration illuminates and stops extreme motion.
ISO should not be too high, because it can increase the effect of the continuous ambient room light.