This is an aerial surveillance film with extended sensitivity in the red range. Due to the specific conditions it is intended for, its speed rating is not according to the ISO standard we are used to, but according to EAFS. The official rating is in the range of 125 to 250. Besides the rating being according to a different standard, the target values for contrast and density are also not what we like. We definitely don't want that contrast...
I would shoot it as 200 ASA -5 or -6 stops depending on the scene with a 720 nm filter.
Bingo
There is more infrared light on a sunny day, so use 400 ISO if the sun is out to avoid over exposure and 200 ISO on a dull day.
If you use film like this for IR, exposure would have to be 5-7 stops more than box speed because IR just doesn't do much. Consequently, the reason of the box speed confusion is not the amount of IR in the light. It's mostly related to the intended gamma as indicated above by
@lamerko.
Moreover, it would be the other way around - on a cloudy day, the
relative component of IR in the entire spectrum is
more than on a sunny day:
(
source)
The influence of IR on total exposure depends a bit on how you define IR; if you define it as anything above 700nm (where human visibility reaches virtually zero), it's a small part of the integral exposure; if you define it as >740nm (popular cutoff of IR filters for our purposes) it's just a sliver:
The yellow + red parts are maybe 25% of the integral exposure; that means effectively a difference between let's say EI200 and EI250 or so if you include or entirely exclude that part of the spectrum (which is a very different and much more extreme scenario than the more subtle relative attenuation of cloudy vs sunny!) The red part (>740nm) is something like 5% of the total exposure, so the effective impact on film speed between sunny & cloudy would effectively be negligible.
Hence, you can work out fairly easily that the IR difference between a sunny our a cloudy day would have only a very slight effect on total exposure, with the cloudy day resulting in a higher effective film speed than the sunny day, and none of this being a good explanation of an entire stop in film speed rating. There's a more problematic aspect to this proposition, and it's the fact that the relative distribution of spectral flux actually does not change all that much between cloudy & sunny conditions - grasping back on the spectral plot I've quoted before, the same article also shows a normalized plot for these conditions, which shows that the relative distribution is really virtually the same:
You could try to make a case for broad daylight vs. dusk/dawn, which would have more of an effect. However, that would make for an apples & oranges comparison as you'll be changing the entire spectral distribution and not just the IR part. For the same reason we don't use different ISO ratings for regular B&W film for broad daylight vs. early mornings & late evenings, we shouldn't do it here with a film that happens to have a little IR sensitivity.
For the real reason, refer to the datasheet here, specifically the curves shown below:
https://www.agfa.com/specialty-products/wp-content/uploads/sites/8/2017/06/AVIPHOT-PAN-200.pdf
Note how the effective speed is roughly 125 to 250...
...but that's for a gamma that's over 1.0, whereas for general photography, we generally aim at something like 0.6-0.7.
The reason for the optimistic speed rating of 200 (let alone 400) is therefore mostly due to a situation that's akin to 'push processing'; an aerial imaging scenario is effectively a low-contrast situation, so the film is developed to a high contrast to compensate for the low SBR (scene brightness range). The result is that the speed point is bumped a little, too (see HD curve family on page 5 of the datasheet; you can plot the ASA speed point in there and see how it moves a little).
Taken together, the rating of 250 is the best-case 'wind in the back, sun in your face' scenario for the film developed to the maximum gamma
for its aerial imaging application, and the 400 rating is a marketing fudge factor added on top of it because hey, it looks good in the sales pitch and shucks, who gives a hoot anyway what speed it really is. Developed for a more usual gamma in regular photographic applications (visible spectrum), you can expect this film to reach no more than ca. ISO 100.