Proof of Work (PoW) and Proof of Stake (PoS) are blockchain consensus (the general opinion about which version is correct) algorithms. These algorithms determine if the miner has completed the required work.
The idea of Proof of Work was firstly described in 1993 in “Pricing via Processing, Or, Combatting Junk Mail, Advances in Cryptology” by Moni Naor and Cynthia Dwork. Authors proposed the idea that a user who wants to access a shared resource must compute some function that will protect the resource from abuse. The function should be complex enough, but feasible.
The term Proof of Work appeared in 1999 in the article “Proofs of Work and Bread Pudding Protocols” by Markus Jakobsson and Ari Juels. After that, PoW began to be used in the blockchain as a way of reaching consensus. PoW provides the ability for a node to verify that the miner has actually performed the necessary calculations to find the block hash. The reward, in this case, is received by the miner who first calculates the hash correctly.
Proof of Stake is an alternative consensus algorithm that appeared in 2012 in the PPCoin (Peercoin) cryptocurrency. The idea is to use “stake”, which determines which node can mine the next block. The complexity of this algorithm is proportionally distributed in accordance with the balance of each node in the network (with the number of coins on user accounts). So, the more cryptocurrency a user has on the account, the greater is the chance of generating the next block.
There is no common opinion which of the algorithms is more reliable. Most serious cryptocurrencies use PoW, although PoS is easier to implement. Some cryptocurrencies use hybrid models of consensus algorithms, or use them consistently. For example, PoW at the stage of classic coin mining and PoS after the completion of the issue.