I always thought it refers to the method of resolving conflicts within a blockchain network's consensus specification:
If there are multiple versions of blocks that are deemed valid by nodes consensus rules, but trying to extend the chain from the same ascendant block, then the version with highest cumulative proof-of-work (blockchain tip's
chainwork) shall be considered as the correct version.
All other uses of the term "Nakamoto Consensus" are abusing the term. It's NOT a governance method or anything like that.
Nodes running a consensus-breaking specification would simply ignore PoW of the other chain and create a hard-fork, where each blockchain network would have their own Nakamoto Consensus game, and not affecting each other.
If they shared the PoW algorithm, then the networks would be bidding for the same kinds of hashes, e.g. sha256d miners would allocate their hash-rate to find balance with sha256d networks block rewards market value.
This is simply a free-market mechanism and NOT Nakamoto Consensus.
PoW miners are providers of hashes, blockchain networks are buyers of hashes. It's a business transaction. Every fee-paying transaction is a business transaction with a miner, of course they'd mine their own transactions - after all, each transaction is a payment for their hashes on top of the block reward subsidy.