I have not followed NFTs like this very closely, but my understanding of them is this:
* There is some contract that generates NFTs under some condition (this is the box you mentioned)
* When the condition is met to create a new NFT, it creates one using VRF data, similar to how is described here: https://blog.coincodecap.com/how-to-generate-random-numbers-...
Anyone can make an NFT and stuff the same random number(s) into it that the contract received from the VRF. The difference is in who made thr NFT. Most people wouldn't find an NFT interesting if it's just a random number, made by a random person. An NFT which was produced by a smart contract might be exactly the same, but it is more interesting because some (usually centralized) game or service uses that random number to represent something else. That game or service is only interested in NFTs created by their smart contract.