Shimano shoes: what is the correct equivalence of US and EU sizes? Or, which to trust more?

Shimano seems to have some contradictory sizing information for their cycling shoes. Their EU/US sizing corresponds differently from shoe to shoe, and also with some industry "norms" (if that’s really a thing).

Here are some examples from actual shoes:

vs.

So which is it Shimano, does EU47 = US12.5 or does it equal US11.8? That’s a significant variation. (Plus I’ve never heard of an US size which is not a multiple of ½?)

Wikipedia agrees with the first one, FWIW.

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It took a little hunting to find a Shimano size chart. On "Which Shimano Kicks Are Right For You?" it says "…Shimano offers a useful size guide…" but actually doesn’t seem to include that. But I did find one on their product pages:

(From here, then click "adaptive size spec" – seems to be generic, not only pertinent to the specific product at this link?)

This chart seems to be consistent with the second tag.

All in all, I’m confused. What to make of all this? Am I more likely to get a good fit assuming the US or EU size is accurate?

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Note – obviously the ideal would be to visit a good store and try stuff on; if it fit the number doesn’t matter. But given Covid and maybe limited local availability it would be great to be able to order online with some confidence that a good fit is possible vs. being a waste of time & money.