Consensus answers a single question: when two valid-looking versions of the ledger exist, which one counts? proof-of-work answers with accumulated computation, proof-of-stake with weighted votes from bonded validators, and other designs with committees or delegated sets.
The choice shapes everything a trader cares about: how fast finality arrives, how a chain-reorg can happen, how supply is issued, and how censorship-resistant the chain is.
No mechanism is risk-free. Proof of work concentrates in cheap-power regions, proof of stake concentrates with large operators, and small-committee designs can be halted by a handful of participants. Treat security claims as assumptions to check, not facts.
Related: proof-of-work, proof-of-stake, finality, chain-reorg