Many often associate Proof of Work, Proof of Stake, etc with blockchain consensus algorithm/mechanisms.
I find that association to be inaccurate. Yes, proof of work / proof of stake are mechanisms by which leaders are elected to validate transactions. It is a crucial part in building consensus but not the only thing. For example, in bitcoin blockchain, the longest chain wins -- this to me is also considered as a crucial part in building consensus across the nodes.
As a blockchain nazi, to me, it only makes sense to call the distributed consensus algorithms such as Paxos, Raft, PBFT, etc as consensus algorithm/mechanisms because of its theoretical/mathematical underpinnings.
Why then is Proof of Work, Proof of Stake used interchangeably with Consensus Mechanisms/Algorithms?