BNB is not ERC20 anymore so it is seperated from your ethereum wallet.
Have you tried to contact the Binance? Because if they are just asking an ethereum address for withdrawal of ERC20 from their exchange, then they will allow all ethereum address then Ledger has no problem at all.

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UPDATE:
Note when I tried to generate my deposit address in ZIL from Binance.

https://i.imgur.com/7KOBYi7.png

In your problem for withdrawing your ZIL from binance, it's probably Binance is using Main net of ZIL, which they want a main net wallet address of ZIL. If that so, you will really need a receiving address of ZIL from the main net.

Ask Ledger about adding mainnet of ZIL since as I can see on the list is ERC20 of ZIL that's why you are getting an ethereum address if you are asking for ZIL receiving address and getting an 'invalid address' from binance withdrawal.

Only Zilliqa is available on Ledger Nano S but Bittorent coin is not yet available, you can see it here: Supported Crypto Assets

Check the version of your Ledger Live. Make sure it is updated and active the experimental ERC20 support.

Try to read this: Manage ERC20 tokens
Once you done that, it's stated that you can use your Ethereum address in receiving some ERC20 tokens. Your ethereum address will be the parent of all your ERC20 tokens, just like in myetherwallet.

Seems binance have cheaper fee and you also can reduce fee further by using BNB,but you can't simply pick random exchange and buy random coins.First you need to decide what coin you are going to buy,if you just planning for day trading then binance would be better but you have to learn about the basic indicators like RSI and bollinger bands for getting idea of when to buy and sell.

If you're planning on selling the coins back at some time then use Kraken also if you're going to use Kraken to buy the coins anyway. No need to unnecessarily use two different platforms. Just remember to use a non-custodial wallet for safe keeping while you're waiting for an opportunity to sell.

Today, for any operating system, there are quite a lot of applications that can be used to trade cryptocurrencies.  Many cryptocurrency users still buy and sell cryptocurrency using websites and consider it more secure.  But if we talk about applications, it is best to choose the application of those trading exchanges that have a very good rating.  Examples include Binance, Kucoin, and GBX Exchange.