Etherum Classic is itself a result of hardfork. Sometimes it is also referred as Classic Ether.
Callisto is a blockchain technology which runs on the Ethereum Classic protocol. Callisto introduces a cold staking protocol which rewards token holders for being participants.
Cold staking is a way of giving CLO token holders incentives for holding for a specific period of time, allowing them to earn interests without validating transactions as transactions will be achieved by the Proof-of-Work algorithm.