In this, you'll get a very brief view of rollups, zkRollups, optimistic rollups, to act as a reference text for the layman. We'll start from the bottom Lego blocks then work our way up to more complex Lego pieces.
The root of the technologies is a computer science innovation called zero-knowledge proofs, which does exactly as its name suggests- it provides proof of something without revealing that specific something.
ZK SNARKS: Succinct Non-interactive Arguments of Knowledge, are an extension of this- it can be used to prove a secret key without actually revealing the key.
ZK Range Proof: prove that a number is within a given range without revealing that number, can be used to find out if someone qualifying for a loan is within $1,000-$99,999 without them revealing the amount.
These are chains that basically mimic the L1 EVM (plasma chains), confirm transactions on their own network, then add the batched transactions to the main Ethereum network for confirmation.
Depends on validators (PoS) who submit batch transactions to L1 and fraud-proofers (also PoS) who determine if a batch of transactions is fraudulent. The downside to this is the time to withdraw (TTM) is longer (a week).
Every batch posted on L1 includes a cryptographic proof (zkSNARK) that can be verified by the L1 contract when then transaction batch is submitted. These rollup transactions do not rely on dispute resolution like their optimistic counterpart. The TTM from an L1 is available immediately after the rollup is complete. These are basically a better version of optimistic rollups, but much harder to implement.