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Reference: http://www.btcsatoshi.com/http://ethdocs.org/en/latest/ether.html

Proof of Stake has the same goal as proof of work—to validate transactions and achieve consensus in the chain—and it uses an algorithm but with a different process. With proof of stake, the creator of a new block “is chosen in a deterministic way, depending on its wealth, also defined as a stake.” Since in a proof of stake system, there is no block reward, but the miners, known as forgers, get the transaction fees. Proponents of this shift, including Ethereum co-founder Buterin, like proof of stake for the energy and cost savings realized to get to a distributed form of consensus.  Reference: http://www.hl.co.uk/news/2018/2/16/a-brief-history-of-blockchain-technology-everyone-should-read

A Byzantine failure is the loss of a system service due to a Byzantine fault in systems that require consensus. Reference: https://en.wikipedia.org/wiki/Byzantine_fault_tolerance