Only BUSD on Ethereum (ERC-20) is issued by Paxos. The BUSD on the BNB Chain (BEP-20) is not affiliated with Paxos and not regulated by NYDFS. Quoting Paxos:
"BUSD is issued by Paxos on the Ethereum blockchain and regulated by the New York Department of Financial Services. Separately, Binance wraps BUSD and issues separate tokens (known as Binance-Peg BUSD) on several blockchains, including BNB Smart Chain, Polygon, and Avalanche. These tokens are unaffiliated with Paxos and not regulated by the NYDFS."
Yes, but I believe that this "wrapping" should be visible on chain. In the sense that there should be a 1:1 mapping between "real" BUSD locked on Ethereum and the number of pegged BUSD on other chains, and that the accounting can be verified in real time. But I haven't verified.
I visited Binance's main page on BUSD [1] and it suggests you go look at their proof-of-reserves page [2], which lists the exact number of each token on Ethereum (5,334,500,000), BNB (5,315,999,056), Avalanche (11,500,000) and Polygon (6,000,000), each with links to block explorers. Note that if everything adds up, this total leaves 1,000,944 tokens on Ethereum, but at least that's positive.
Edit: I spent some time thinking the Ethereum number was the total number of BUSD, but apparently it is Binance's holdings which can be found in a wallet nicknamed "Binance: Binance-Peg Tokens" on Etherscan [3]. Since this number is greater than the total number of pegged tokens, I guess everything adds up. (Of course, since the "cross-chain peg" here is implemented in a centralized way by Binance, it could de-peg at any point they want it to.)
Only BUSD on Ethereum (ERC-20) is issued by Paxos. The BUSD on the BNB Chain (BEP-20) is not affiliated with Paxos and not regulated by NYDFS. Quoting Paxos:
"BUSD is issued by Paxos on the Ethereum blockchain and regulated by the New York Department of Financial Services. Separately, Binance wraps BUSD and issues separate tokens (known as Binance-Peg BUSD) on several blockchains, including BNB Smart Chain, Polygon, and Avalanche. These tokens are unaffiliated with Paxos and not regulated by the NYDFS."