Can the term Nakamoto Consensus (NC) be used interchangeably with Proof of Work (PoW)? Which term would the community prefer to use?
Algorithms for achieving consensus with arbitrary faults generally require some form of voting among a known set of participants. Two general approaches have been proposed.
The first, often referred to as “Nakamoto consensus”, elects a leader through some form of “lottery”. The leader then proposes a block that can be added to a chain of previously committed blocks. In Bitcoin, the first participant to successfully solve a cryptographic puzzle wins the leader-election lottery. The elected leader broadcasts the new block to the rest of the participants who implicitly vote to accept the block by adding the block to a chain of accepted blocks and proposing subsequent transaction blocks that build on that chain.
The second approach is based on traditional Byzantine Fault Tolerance (BFT) algorithms and uses multiple rounds of explicit votes to achieve consensus. Ripple and Stellar developed consensus protocols that extend traditional BFT for open participation.
So, Nakamoto consensus is in my opinion a synonym for Proof of Work, as it involves some kind of randomness in finding a valid hash, which is meant by "lottery" in the description above.
Nevertheless, I personally would stick to Proof of Work as it does not confuse people, who maybe do not know, that it was Satoshi Nakamoto who introduced Proof of Work as a consensus mechanism.