"Physical of relevance" to what? If you need a part that you can trust to operate down to -40C, then you need to use a part spec'ed for that, if not, then you don't.
The part with the wider temp range may or may not be substantially different from the other one, but the only guarantees are what the datasheet says. It may be that the parts have no real differences except that one is tested and qualified to a higher standard (which actually is more expensive, hence the higher price), and the lower spec will work fine at -40C. It may even be that the manufacturer will bin parts based on performance/demand, and you may order the lower spec part and get a higher spec part if the manufacturer overproduced those and down-binned them, but there's no guarantee that will happen every time you order them.
Using a part outside of the limits given in the datasheet may cause immediate failure, or it may work fine, or it may work fine with *this* batch of parts but not *that* batch of parts, or 99.9% of parts may work but that last 0.1% may fail at the worst possible time. If it's a one-off project that lives on your bench, sure, give it a try, not a big risk if it breaks. If you're shipping a million units out all over the world then you better do your homework to make sure that you're choosing parts that will be reliable, and you go outside the datasheet limits exclusively at your own risk.