Not really. The key difference is the degree of involvement Bitcoin miners have in Stacks mining. In side-chains, Bitcoin miners would need to opt-in to mining the side-chain and validate its blocks. In Stacks, Bitcoin miners only need to include the Stacks miners' block-commitment transactions into Bitcoin blocks. Since block-commitment transactions look like normal BTC transactions, no Bitcoin miner involvement is necessary beyond what they're already doing.
From their site:
> Like Bitcoin, Stacks is a layer-1 blockchain. Proof of Transfer connects it to Bitcoin with a 1:1 block ratio.