Which crypto are you trying to withdrawal?
If you want to withdrawal BTC to your Nano S, you need to use the BTC chain (which is the real one, where the real BTC is located).
If you want to withdrawal ETH to your Nano S, you will need to use the ETH (ERC20) chain.
The same way, if you want to send BTC to another exchange, ecommerce, friend, etc... you will have to select the right (and compatible) chain, which 99% of the time is just their native chains. Basically, only Binance itself accepts BNB and BSC chain coins.
Both BNB and BSC are different chains created by Binance, so they are not really Bitcoin (or Ethereum, Ripple, etc...). The BTC in there is basically an
IOU where they promise you that you can give them 1 BTC on the BNB chain and receive 1 BTC on the real chain. Basically, it's a side chain you can use to transfer coins from/to compatible wallets/exchanges while not actually moving them in the real chain, and thus paying less fees.
I have some BNB that I could use to keep the fees down
The BNB token only lowers your fees when trading on Binance, not when withdrawing. Unfortunately, Binance's fees on Bitcoin are outrageous, so there isn't much you can do if you want to take them from there through the BTC chain.
edit:
Really, really careful with that:
I don't think you will get any warning about the addresses if you entered the right address.
You also don't get a warning if you use any ETH address (0x...) to withdrawal through the BNB or BSC chain. But both can result in the loss of your coins if you send BNB/BSC coins to someone that doesn't support it (99% of all ecommerces/services).
For example, you can withdrawal LINK through the BNB or BSC chain to Coinbase, but that will result in the LOSS of your coins.