I don’t fully understand how current Layer 2 blockchains are “linked” to the Ethereum blockchain

So from what I understand, L2s are completely separate blockchains that allow protocols to migrate to the separate blockchain without having to change the code/design.

I understand how rollups are connected to the L1, which L2s are currently using rollups? And what makes a layer 2 different to any other blockchain that is EVM compatible?

Thanks.