Yes, optimistic rollups operate differently from zk rollups.

If we start with the similarities, both optimistic and zk rollups:

The difference comes in when we consider how they verify that a transaction on the rollup was valid.

Optimistic rollups assume all transactions are valid (hence "optimistic"). They rely on actors searching for invalid transactions in the transaction data that is posted back to the main chain. If an invalid tx is found, whoever found it can post a "fraud proof" that demonstrates it is invalid. If their fraud proof is successful, then the validator that included the invalid tx gets slashed.

Zk rollups operate differently. They rely on zero-knowledge proving systems to ensure that transactions on the rollup are valid. Through some cryptography wizardry, zk proving systems produce a "proof" to go along with each tx that shows it was executed correctly. Given the start state, the end state, and a proof, a verifier can validate that each tx was executed correctly.

So, the big difference is that zk rollups verify every transaction on the rollup whereas optimistic rollups only verify transactions when a fraud proof is submitted.

If you want to dive more into these two topics, I recommend Ethereum's developer docs on each: