Bitcoin originated smart contracts, but they were severely limited due to a filter that was imposed. Arbitrary scrypt execution was seen as a security risk (despite not being Turing-complete), so a set of scrypt templates were whitelisted. I think all clients would accept blocks with any scrypt in them, but most pools would only accept transactions with the fixed templates.

Bitcoin does have enough flexibility to do trustless cross-chain trading though, so it's possible to do dapp logic in Eth and manipulate BTC funds indirectly. (IIRC)