Yes, Tether (USDT) is a multi-chain token available on multiple networks (blockchains). Tether has been issued on the Omni, Ethereum, Tron, EOS, Liquid, Solana and Algorand blockchains (and maybe on some others I don't know).
The first tokens were issued on the Bitcoin blockchain by using the Omni Layer Protocol.
USDT-ERC20 is the USDT based on the ERC20 protocol with deposits and withdrawals taking place on the ETH network.
Similarly, USDT-TRON (TRC20) is the USDT based on the TRC20 protocol. The currency deposit address is the TRON address, with deposits and withdrawals taking place on the TRON network.
reference: https://community.trustwallet.com/t/tether-usdt-trc20-vs-erc20/61950
Likewise, there is also the USDT on EOS, Solana, Algorand and Liquid, yet the most used are ERC20 and TRC20.
Just make sure both the sender and the receiver support the selected protocol, and that the deposit address is correct.