The main technical difference between Polygon and the rollups is in how they store the data:

1. Polygon operates as its own blockchain, where the block producers (validators) also commit checkpoints on Ethereum so that somebody following Ethereum blocks can synchronize with the Polygon blocks. This makes it possible to know that the Polygon chain did not get its history rewritten between checkpoints.
2. Optimism and Arbitrum basically execute and compress their transactions into a single chunk and commit it directly to Ethereum. They're called "roll-ups" because they "roll" a bundle of transactions into a single block.

Looking from the Ethereum side, the semantics are basically the same. At some point in time, the Layer 2 (regardless of Polygon, Optimism, Arbitrum, etc) received transactions that were executed off-chain and the results recorded. Whether these be stored "off-chain" but on a different chain (Polygon), or compressed into a more dense form (rollups), they're all effectively a blockchain running in parallel to Ethereum.