I think those 2 things are very different. Does this mean that for every Dapp with Lisk one has to download another sidechain blockchain?
Lisk blockchain applications are different from Ethereum smart contracts, although Ethereum Virtual Machine (EVM) can run as a Lisk app with its own delegates.
Lisk apps run as sidechains which can receive and send Lisk from a multisig address on the main Lisk chain.
They can use Delegated Proof of Stake like the main Lisk chain, but with their own set of delegates, or they can use a different consensus mechanism.
Whether or not the user of a Lisk blockchain app has to download the sidechain for that app depends on how the developer designs the client and GUI for that app.