TUSD is built on the Ethereum blockchain and is an ERC-20 token. TUSDB is built on Binance Chain, a separate blockchain, and is a BEP-2 token. They serve the same functionality - digital versions of U.S. Dollars that are backed 1:1 by a physical U.S. Dollar held in an escrow account.
The primary difference is that they are built to be compatible with their respective blockchains.
An applicable analogy would be how the Facebook app has similar functionality on both iOS and Android operating systems, it functions the same but the developers had to build each version according to the specific technical requirements of each operating system.