Counterparty and OMNI are protocol layers built on top of the Bitcoin network. These layers allow for the issuance of tokens.
From the Counterparty documentation: "Custom Counterparty tokens can be used for a wide range of purposes and act as their own cryptocurrency, while still running on the Bitcoin blockchain. Unlike ordinary bitcoin, custom tokens can be used to represent any kind of value".
OMNI is similar, claiming that "Omni is a platform for creating and trading custom digital assets and currencies. It is a software layer built on top of the most popular, most audited, most secure blockchain -- Bitcoin. Omni transactions are Bitcoin transactions that enable next-generation features on the Bitcoin Blockchain".
ShapeShift Supported BTC Tokens
Some Counterparty tokens include Storj (SJCX), BitCrystals (BCY), and the CounterParty native token (XCP). OMNI assets that ShapeShift exchanges include Tether (USDT) and OMNI. You can exchange these BTC tokens here.