I think that quiz would like you to buy two of their products, which is a thing you might want to do (I'd suggest maybe one of theirs and one from a rival, but they're not going to suggest that) but it is not implying those keys are identical inside, they are as you say "independent keys".

So you'd register both keys. Or if you own more, you'd register at least two of them and at least one stays somewhere safe (but like, not in a bank safety deposit box, maybe the sort of place you keep a passport). This way, when inevitably your toddler throws mummy's key ring into a fast moving river, it's just very inconvenient and doesn't ruin your whole year. After you call somebody to bring a spare car key, and ask the toddler to think about what they did, go revoke all those now useless keys and order a new FIDO authenticator.

Edited to add: Even if they started identical you can reset any Yubikey, making the keys inside it random - and very paranoid people might want to before using it, since you don't know what happened to the keys inside it before you got it.

The existence of a cloned physical key is not possible due to FIDO U2F protocol. Every sign operation increases a counter on the device. It's supposed that services will keep track of this counter and don't accept signatures with an incorrect counter (less than known).