PoPP = Proof of Processed Payments
Proof-of-Processed-Payments (PoPP) is how Metal aims to distribute MTL to the masses. Think of it as a human-powered Proof-of-Work (POW), as opposed to a computational-powered PoW, such as the one Bitcoin uses.
PoPP acts as a provable way of identifying users and distributing new currency into the system. At the same time, it rewards users who convert fiat currency into cryptocurrency. When a payment is settled, a portion of the gross amount of the payment is returned in MTL.
The amount received is up to 5% of the volume of the transaction at trading value for MTL in either direction (sender/receiver). Consider as an example that Alice sends Bob $100 using the Metal Pay app and at the time MTL is trading at $1 per MTL. Following confirmation of a successful transaction, both Alice and Bob would receive $5 in MTL, which in this case would be 5 MTL.
More information on PoPP is available here.
PoW = Proof of Work
Bitcoin, which made the blockchain technology popular, developed the so-called "Proof of Work" (PoW) algorithm. In principle, each participant on the Bitcoin network can participate in the block generation. In order to confirm the transaction and enter a block into the blockchain, a miner has to provide an answer, or a proof, to a specific challenge.
Miners use PoW to validate transactions and mining new coins, but its main goal is to block potential cyber-attacks or suspicious activities within the network. Each time a miner confirms a transaction, he is rewarded with Bitcoin(s). The disadvantage of this algorithm is that it consumes large quantities of electricity.
PoS = Proof of Stake
Proof of Stake is a proposed alternative to Proof of Work. Proof of stake (PoS) is a type of algorithm by which a cryptocurrency blockchain network aims to achieve distributed consensus. In PoS-based cryptocurrencies, the creator of the next block is chosen via various combinations of random selection and wealth or age (i.e., the stake).
In contrast, the algorithm of Proof of Work-based cryptocurrencies such as Bitcoin uses mining; that is, the solving of computationally intensive puzzles to validate transactions and create new blocks. Source: Wikipedia