First though, it is anachronistic and incorrect to refer to any pre-standard crank or BB taper as "ISO" or "JIS", because those standards simply didn't exist until around 1991. Before standardization, companies' tapers were proprietary, and though the taper angles are (almost*) always 2°, the square end size, and the length of the tapers are different. Even after standardization, companies were/are free to ignore the standards; compliance is voluntary. So don't make the mistake of thinking ISO and JIS are the only two tapers out there, even on post-1991 parts.

Now regarding the two standards:What is known as the JIS standard started as the Sugino "Maxy" taper, used by practically every far-eastern manufacturer for the vast majority of their cotterless cranks. It's close to the TA taper, in fact. But it is also similar to the Stronglight taper, except that the Stronglight taper was asymmetrical (longer on the right than the left), while the JIS/Maxy is symmetrical, as was TA. (Interestingly, according to Stronglight's web page, all their current square-taper production is JIS standard, while TA's is ISO. Not sure if this has always been the case with post-1991 Stronglight though.)

Per JIS D 9403:For a nutted axle: the same except the taper flat length is 16mm minimum.

Most high-end Japanese cranks, before and after JIS, did not use the Maxy/JIS taper. Early Dura-Ace, Sugino Mighty, and Suntour Superbe cranks notably had tapers much closer to the Campagnolo taper (but not always identical.) Sugino now calls the "Mighty" taper the "75" taper, and it's still used on their excellent traditional 75 cranksets. It is not ISO, nor is it JIS low-profile. Not to say it wouldn't work with other tapers, but it is its own thing.

The ISO taper is NOT "based on" the Campagnolo taper, rather it is a compromise taper intended to be functionally compatible with as many pre-standard European crank tapers as possible. The pre-standard Campagnolo taper starts bigger than ISO, is shorter, and is symmetrical. TA is a bit bigger still, and symmetrical. The Stronglight taper starts even bigger, but as noted, is asymmetrical. The ISO taper starts smaller than all three, so as to be able to work with Zeus, Nervar, and possibly even Ofmega cranks, but is asymmetrical, being again longer on the right side, so as (hopefully) to be compatible with Stronglight and TA cranks. Being a compromise, ISO is not a perfect fit for any.

After its adoption, AFAIK most surviving European crank and BB manufacturers followed suit, including TA and Campagnolo (who were practically the only remaining ones of consequence, and almost certainly had a hand in the formation of the standard.)

Per ISO 6695:1991:(This was revised in 2015, but I don't have access to the revision.)

That said, some BB manufacturers make both tapers, so either check documentation, or measure the square end (across flats) and taper length to determine. Note that the JIS square end is measured at the spindle end, while the ISO is measured 1.5mm from the spindle end. Because of the taper, an ISO axle will be measurably smaller at the end than a JIS. As Stephen said, one measurement is worth a thousand expert opinions.

Note that Phil Wood made their own compromise taper back in the day. It was between the Campagnolo, Stronglight, and TA, and intended to work acceptably with them all. Now they make only the modern standard tapers.

Greg Reiche
CA USA
*Sakae made a 3° taper crankset and BB for a while. Rare, thankfully.