I would to buy the very old one Bitorrent not the new Bitorrent. And I am still not sure whether BTT old is BTTC.

And what's the benefit of buying the old token if the project has already moved on and the BitTorrent ecosystem now relies on the new BTTC token? Since the launch of the mainnet in 2021, the old BTT tokens on TRC10 were migrated to the new BTT (BTTC on Binance) on TRC20.

For more detailed information, you can visit the following sources:
[1] Launch of BTTC Mainnet and BTT Redenomination Plan
[2] Clarification on BTT Redenomination Plan Supported By Exchanges and BTT Renaming

So do you mean that if I want to buy old BTT, I can just buy BTTC as both are identical?