Clients are software packages that can be used to run the Ethereum Classic protocol in various modes; Full Nodes, Archive Nodes, Fast Sync Clients, etc. Clients allow you to run a mainnet or testnet node, validate blocks through mining, and interface with the network through API.
You can find additional tools to help manage client deployments in the tooling section.
Core-Geth is a distribution of go-ethereum with many flavors. This client is Long Term Supported by the ETC Core development team, and is a recommended client from a well-known transparent team.
Hyperledger Besu is an Ethereum client designed to be enterprise-friendly for both public and private permissioned network use cases. This client is Long Term Supported by the ChainSafe and ETC Cooperative teams as part of the Hyperledger project with stable funding from Grayscale's Ethereum Classic Trust. This is a recommended client from a well-known transparent team.