single purpose blockchain: The ledger only holds effectively 1 type of information, transactions (~ who owes what to who, without any meta data)
Proof of work - To decide who gets to create the next block in the chain with all the information of the last transactions (and thus ratify as source of truth) the chain's algorithm looks at who has most skin in the game. As a proxy it looks at the amount of work block 'miner' commit to the blockchain project. Proof is provided by having 'miners' do work, in Bitcoin's case complicated equations is the work. Solving these equations cost a lot of computing power, and therefore energy. However there is also a randomness involved to assigning who gets to create the next block, therefore it is hard to game.
2nd generation: e.g. Ethereum
Multipurpose blockchain: The ledger can hold multiple types of information in paralel, so for example cash (who owes what to who), as well as Smart Contracts (an algorithm with a set of rules).
Proof of work - Proof is still provided by having 'miners' do work
3rd generation: e.g. Cardano, Solana, Avalanche
Multipurpose blockchain: multiple native tokens and smart contracts. Typically 3rd generation chains are also tackle issues of scale (transactions/sec) and transaction cost from the outset
Proof of Stake - Proof is provided by people pooling their money together in a pool. If people commit (stake) a lot of money to a pool that is taken as a proxy for how much skin they have in the game, and therefore as guidance for priority in creating the next block.
While IOTA is technically not a blockchain, it's an interesting adjacent technology. IOTA uses a 'tangle' structure, also quite ingenious but does not have some of the key security and smart contract functionalities.
Note that a lot of new types of proof are developing rapidly depending on the purpose or a blockchain, for example Proof of Signal (based on your wifi reach), proof of history (based on past transactions), etc. etc.