Tethers exist as digital tokens built on bitcoin (Omni and Liquid Protocol), Ethereum, EOS and Tron blockchains. These transport protocols consist of open source software that interface with blockchains to allow for the issuance and redemption of cryptocurrency tokens, in this case, "tethers."
Tether was originally created to use the Bitcoin network as its transport protocol—specifically, the Omni Layer—to allow transactions of tokenised traditional currency. Since this original version of Tether uses the Bitcoin blockchain it inherits the inherent stability and security of the longest established blockchain network.
Tether on the Ethereum blockchain, as an ERC20 token, is a newer transport layer, which now makes tether available in Ethereum smart contracts or decentralised applications on Ethereum. As a standard ERC20 token it can also be sent to any Ethereum address.
Since Tether is currently available using different transport protocols, when users send tethers to other addresses, they need to carefully check the destination address to confirm they are selecting the correct transport protocol.