The HSS insight needed is that while HSS may appear to humans as a quick flash, HSS is in fact a longer flash, and actually is a "continuous light". The shutter definitely sees HSS as being continuously "on" for the entire shutter duration, from before the shutter opens until after it closes, same as it sees sunshine or incandescent lights as being continuous light. Continuous light eliminates any sync requirement, allowing any fast shutter speed. In that way, HSS is High Speed "Sync", but is NOT at all high speed "flash". Being continuous, HSS flash has absolutely no speed stopping capability at all. The faster shutter speed may help, but speedlight mode can be greatly faster than any shutter speed. Like any continuous light, the HSS exposure is greatly affected by the short duration of that shutter speed. Fast shutter speed reduces the HSS flash exposure greatly, so aperture must be opened to compensate that loss (HSS is exactly the same as continuous sunlight in that regard, equivalent exposures work for HSS too). HSS can only run continuously at reduced power level. The Nikon HSS Guide Number is less than half of speedlight mode GN, meaning the distance range approaches half, but the HSS power is closer to 1/5 or 20%... about 2.3 stops down from speedlight mode. We could gang five flashes (acting as one) and get the stops back. Reality is that speedlight mode runs circles around HSS indoors (in speed, power, range), so we could only consider using HSS shutter speeds in bright sun as fill (fill flash level does not require as much power).
See What is HSS Flash.
In strong contrast, regular speedlight flash exposure is independent of shutter speed (the flash duration is typically much shorter than the shutter speed duration). The shutter merely needs to be fully open (which is the "sync" requirement). However both sunlight and HSS flash are also continuous light, so fast shutter speed of course reduces their exposure, both the same way. It's natural, we expect that. For either or both sun or HSS, we can open the aperture wider to compensate, which creates the concept of Equivalent Exposure (same as for sunlight). If shutter speed is twice as fast, we simply open aperture one stop to recover. Any equivalent exposure is still the same exposure, true for both sun and HSS flash, but not at all true of speedlight flash mode.
This calculator on this page is for HSS. The version for regular flash mode is on the previous page. This version does offer either option, but all of the page text supporting regular flash mode is on that first page.
The distance can be your choice of either feet or meters, but the GN for feet is 3.28 times greater than the GN for meters.
And of course, HSS mode uses a lower guide number than regular flash mode.
The Speedlight Mode version of this same GN calculator disables the shutter speed aspects, and advises you that the Guide Number should also change when switching modes. And then it works for speedlight mode, but of course, there are no Equivalent Exposures in speedlight mode. For example, the Guide Number in Nikon speedlights is maybe typically around 2.33 to 2.67 EV higher than HSS mode (HSS must be lower level to be able to run continuously).
Assuming the camera has a 1/200 second sync speed, shutter speeds of 1/200 second or slower will not use HSS mode, so those will be speedlight mode, and this becomes the wrong calculator mode then. On the camera models with 1/250 sync, then 1/250 is NOT HSS mode, and then in a few cases, 1/320 second can be not HSS.
Insufficient flash exposure is corrected with more flash power, higher ISO, wider aperture, or shorter distance, or for HSS, slower shutter speed.
Excessive flash exposure is corrected with less flash power, lower ISO, stopped down aperture, or longer distance, or for HSS, faster shutter speed.
Doubling ISO or power level increases exposure 1 EV.
Doubling HSS shutter speed reduces exposure 1 EV.
Doubling Guide Number increases flash exposure 2 EV.
Doubling f/stop number or distance reduces flash exposure 2 EV.
Equivalency applies to both HSS flash and sunlight (applies to any continuous light). This is a big deal. Example is a D800 and SB-800 at 5.5 feet, at ISO 400 and 24 mm, hot shoe direct flash. HSS flash is at manual Full power level. The Guide Number is GN 72 feet at reference 1/300 second if at ISO 400, so f/16 1/320 worked for the ambient alone (Auto FP 1/250 mode). The 1/300 seems an odd value, very near a quarter stop, and near 0.1 EV from 1/320, however it rounds to 1/320. So at f/16, HSS GN distance is 72/16 = 4.5 feet. Using 5.5 distance instead of computed 4.5 was a flash reduction to become a lower fill level in daylight (computes 122% distance, roughly -0.6 stop). Both flash and sunlight have the same results at f/16 1/320 second and also same at f/4 1/5000 second with HSS flash (equivalent exposures, ISO 400). This is a Big Deal, HSS works with the same Equivalent Exposures as Daylight (because both are continuous light). Specifically, this means the same one HSS GN works at any Equivalent Exposure (up and down the camera P mode range), which is very useful to know when using HSS flash.
The Nikon flash manuals have a separate Guide Number chart for HSS (GN is for bare direct flash.) Typically, the later models (SB-900, SB-700, spec chart in rear of manual) give 1/500 second shutter for HSS GN. Earlier models (SB-800 page 106, SB-600 page 76) give it as 1/300 second, but since then, the maximum sync speed became faster. Since HSS is continuous light, this means we can use any Equivalent Exposure to shift HSS away from this referenced shutter speed number (and the HSS GN remains the same for any equivalent exposure). The GN Calculator could add an input of HSS Shutter speed is ± Stops different than the one specified for GN rating, however the concept of Equivalent Exposure is much stronger to use.
For example, if the HSS GN is 36 at 1/300 second (from the SB-800 HSS GN chart next below, 24 mm ISO 100, feet), then HSS exposure for 10 feet is 1/300 at 36/10 = f/3.6. Then any equivalent exposure of 1/300 f/3.6 works the same at 10 feet for HSS, for example 1/1200 f/1.8 is the same GN, same distance, same exposure (you can get more GN and more flash range and higher equivalent shutter speeds by converting to higher ISO, ISO 400 is 2x GN). Both sunlight and HSS are continuous light, so both work this same way (equivalent exposures are the same exposure). The beauty is that changing equivalent exposures won't affect your flash or sun exposure, or your HSS fill ratio. The problem is that HSS guide numbers are quite low.
Some flashes do offer the HSS Guide Number chart in their manual, and this chart will also specify the shutter speed at which it is applicable. This is the SB-800 HSS GN chart (page 106 PDF manual). Older SB-600 and SB-800 models used this 1/300 second reference, the newer SB-700, SB-900, SB-5000 models use 1/500 second. The 1/300 is an awkward shutter number, I call it 1/320 second (only about 0.1 EV difference). The idea is to compute HSS GN settings for that referenced shutter speed, and then any equivalent exposure works the same (for HSS or sunlight, or both).
So repeating, HSS GN is different, and easy, but a little tricky. Shutter speed does not affect speedlight GN, but shutter speed of course does greatly affect HSS GN. This older GN chart says it is for 1/300 second (1/500 second is more common to see today). HSS has Guide Numbers, for the specified conditions stated. Here 24 mm ISO 400 is GN 72 specified at 1/300 second. So for 1/320 f/16, maximum TTL power is range GN72/f16 = 4.5 foot range (because, in this case, the shutter speed matches the stated situation). This tree is a foot farther, so it's down about -0.6 EV here (let's call it fill flash). But this same 4.5 distance is applied to Any Equivalent Exposure, so 1/5000 f/4 is the same 4.5 foot range.
IMO, HSS can be a mixed bag in the Chinese flashes. Nikon does a good job showing more specifications in the manuals, and they're accurate and work. Here's the Nikon SB-700 HSS GN chart (there's a chart for DX mode too).
Other brands, specifications may be much harder to come by. You can determine the guide number by finding correct full power exposure for your test case (which case also includes the specific zoom value, ISO, and also a shutter speed for HSS mode). Repeat this test in a couple of situations to see the variance. Then for that correct exposure, Guide Number is f/Number * distance that gives the correct exposure (use f/4 or f/8 which are more precise numbers). See the previous GN page.
For HSS flash GN, compute HSS range for the specified shutter speed, and then any Equivalent Exposure is equivalent, with same range, specified at one shutter speed. It means that 1/5000 second is -4 EV from 1/320 second (1/16 of exposure), so for 1/5000 second, we open the aperture 4 stops, then with same range of the same Equivalent Exposure and same GN.
However in sunlight, our exposure also has to match the suns ambient exposure. Then any Equivalent Exposure responds the same for both sunlight and for HSS flash.
But assuming bright sun (if we are using HSS), then fill flash level only needs to be a stop or two less than full illumination level, and if assuming -2 EV fill, that fill concept doubles the GN distance. That range becomes 15.6 feet for -2 EV fill, which is 20% TTL flash. A -1 EV flash compensation is 1.4x GN distance, and 33% TTL flash. This level at higher ISO can be usable for f/1.8 portraits at reasonably close range, but sports action will generally be too distant.
(More about HSS here). I can't imagine even considering HSS indoors (speaking of normal room lighting). Because speedlight mode can run circles around HSS indoors, power, range, and speed for motion stopping (is why they are called speedlights). Yes, speedlight mode is limited to maximum shutter sync speed... which won't matter indoors, because ambient is typically well underexposed indoors (underexposure cannot blur much). The flash is typically much faster than the shutter.