More information is needed from you OP to figure out what happened here or what most probably happened.
First of all, I have never heard of Binance converting any assets on their own. There is an option to convert your coins to BNB, but you have to do that manually. Binance doesn't do it themselves. Regarding the address being different than the one you copy/pasted, it could be proof of a clipboard virus. It's easy to check it you are infected with one. Copy any bitcoin address from your wallet and paste it somewhere. Now, compare the pasted address with the one you copied. If it changed to a different one, you have a clipboard malware on your system. If it's identical, you don't. Most of the withdrawals on Binance are surely automated, so I doubt someone replaced your destination address to steal $15 worth of an altcoin.
Now to the issue with the BTT not appearing in Ledger Live. We first have to figure out how you got a receiving address in Ledger Live if the coin isn't supported?! It doesn't make sense. I assume BTT is BitTorrent, right? If it is, Ledger supports two variants of this token.
The first one is a TRC10 token found on the Tron network. Ledger supports this token and the Tron network natively in Ledger Live. To receive BTT as a TRC10 token, you have to install the Tron app in Ledger Live and send the tokens to your Tron address. Is that what you did?
The second BTT token isn't natively supported by Ledger Live. Which means, you have to use a 3rd-party wallet and connect your Ledger with it. Based on the suggested wallets on
https://www.ledger.com/supported-crypto-assets (MyCrypto and MyEtherWallet), it looks like this BTT variant is an Ethereum token, although it doesn't say that on the page. I don't know if BitTorrent has a mainnet, and if they do, why would Ledger work with MEW and MyCrypto for this wallet. Did you maybe send your transaction to this BTT version (let's call it that)?
What does the blockchain data show? Are the coins you sent from Binance still on the address that received them or were they moved elsewhere? Which blockchain is it?
While we are at it, can you paste here the website address from your browser history where you logged in to Binance and initiated the withdrawal?
OP's silence and the fact that he never returned might mean he understood he made a mistake somehow and gave up. Or it somehow worked out for the better in the end. The latter doesn't happen very often in crypto.