It is important to understand the distinction between BUSD and Binance-Peg BUSD. These are two different products.
Binance USD (BUSD) is a regulated, fiat-backed stablecoin pegged to the US dollar. The Paxos-issued BUSD stablecoin, as well as its reserves, are subject to strict regulatory oversight by the New York Department of Financial Services. BUSD is backed by reserves held in either or both (i) fiat cash in dedicated omnibus accounts at insured U.S. banks and/or (ii) U.S. Treasury bills (including through repurchase agreements and/or money-market funds invested in U.S. Treasury bills).
Binance-Peg BUSD, which is not issued by Paxos and is not regulated by NYDFS, is a separate product. Binance independently mints Binance-Peg BUSD on other blockchains (e.g., BNB Chain, Polygon and Avalanche) and pegs the tokens to BUSD on a one-to-one basis. This allows holders of both tokens to swap tokens between Ethereum and other blockchains.