Blockchain

• A blockchain is a recording of data.
• Blocks can have one or more records.
• Blocks are chained together by the hash of the content of the last block. Except the first (genesis) block all blocks start with the hash of the block it succeeds.
• Any change in any of the previous blocks will change the hash of that block an so break the chain

Consensus Algorithm

A consensus algorithm is used to verify a block's correctness.

• Nodes in the blockchain network verify the blocks.
• A block is valid when the majority of nodes think so.

Nodes must prove they are allowed to participate in the blockchain network. The consensus algorithm defines how a node can do that. These are the algorithms I know of.

• Proof of Work - Bitcoin - Solving a cryptographic puzzle
• Proof of stake - Cardano - Having an amount of tokens (e.g. cryptocurrencies)
• Proof of authority
• Proof of Elapsed time
• Proof of Capacity and Proof of Space
• Proof of Burn