Telos is a new blockchain network based on EOSIO software. Eos and Telos are both networks running the EOSIO software. Any smart contract that runs on one system should run equally well on the other. Telos has modified the Eos genesis snapshot and some rules to make the network more responsible to the majority of token holders, to be more attractive to DApp developers, and to generally run more responsively and sustainably. TLOS is the name of the token that reflects ownership in the Telos network. A TLOS token is like an EOS token except that there will be around 3X fewer TLOS tokens than EOS.
Shardus is building distributed ledger software to remedy the problems of traditional blockchains -- scalability, decentralization and efficiency. The technology being developed will use compute and state sharding to accommodate billions of daily active users, allowing for global-scale decentralized networks.