What is PoW and PoS

Proof of Work(PoW) and Proof of Stake(PoS) are some of the main scripting algorithms that we see at work today mainly in Bitcoin and Ethereum protocols.

Currently both Bitcoin and Ethereum use Proof of Work to determine if the miner does indeed possess a copy of the blockchain and has validated each and every transaction to be in sync with the rest of the Bitcoin/Ethereum nodes around the world.

Its been said that Ethereum plans on switching to proof of stake later in the near future whereas Bitcoin is dependant on a consensus initiative taken through a BIP (Bitcoin Improvement Proposal)

Proof of work and Proof of Stake protocols are mainly present to deter people from performing DDoS attacks upon the the network. 
More insight can be found from my previous article here:
Is it possible to launch a DDoS attack using Ethereum’s blockchain ?

Proof of work determines if the blocks that have been mined by the miner are the same blocks that are present with the majority of nodes across the network. A number of transactions are included in a block and the block is then collectively hashed for this hash to be linked in the next block. Once the block is hashed, the remaining miners aren’t required to find the nonce again but are required to check the validity using checksum thus making way to verify the block in a much easier fashion.

Proof of stake determines who gets to create the next block to link to the blockchain based on their stake within the network. The transactions hence made are said to have been minted or forged in this scenario. The forger of the next block is chosen in a deterministic (pseudo-random) way, and the chance that an account is chosen depends on their stake.

In a much basic version of Proof of Stake, forgers aren’t issued block rewards but are self reliant through the transaction fees paid by the network.

Proof of Work and Proof of Stake are both useful and utilized in our current economic scenario to distantiate people from conducting any sort of action that would be against or hinder what the cryptocurrency in question intends to do or be.

Irrespectively both have their own inbound pros and cons as is the case with anything else.

References:
ethereum/wiki
A Proof of Stake Design Philosophy — Vitalik Buterin — Medium
Proof-of-stake — Wikipedia
Proof of Stake — Bitcoin Wiki 
Proof of work — Bitcoin Wiki
Bitcoin Improvement Proposals

All the very Best :)

I hope this was helpful.

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