Are any road pedal cleats compatible with any road shoes?

I’m switching from mountain biking to road biking and I don’t quite understand road cyclists’ idea of the whole shoes/cleats/pedals interaction.
Say I buy a decent set of pedals, which also come with a set of complementing cleats. Are those cleats compatible with any shoes? I have a pair of Shimano road shoes, and I’m wondering whether the cleat screws are standard?
Thanks.

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