Yes, you can create various collections on different chains. Say there's one on Eth, and one on Binance.

If I want to purchase the NFT, which one should I buy from? Which one should I honor? Well, depends on what I value as a counter-party.

I know that Binance owns all the nodes, and can roll them back at their whim. I know that no one in Eth can roll back easily.

So if I value this kind of immutability as a potential owner of an NFT--I want my transactions to be final--then I'm going to go with the NFT contract on Eth.

There may be other things I value instead of immutability, but the point is just the answer to "which NFT contract on which chain is the 'real one'?" is simply, "The one your counter-party honors, for whatever reason."

There may be instances where both are honored at the same time, but in different domains.