Let's say a torrent website asks the user through an LLM interface what kind of copyrighted content they want to download and then offers me links based on that, and makes money off of it.

The user is "inputting variables into their probability algorithm that's resulting in the copyright work".

Theoretically a torrent website that does not distribute the copyright files themselves in anyway should be legal, unless there's a specific law for this (I'm unaware of any, but I may be wrong).

They tend to try argue for conspiracy to commit copyright infringement, it's a tenuous case to make unless they can prove that was actually their intention. I think in most cases it's ISP/hosting terms and conditions and legal costs that lead to their demise.

Your example of the model asking specifically "what copyrighted content would you like to download", kinda implies conspiracy to commit copyright infringement would be a valid charge.

How is it any different than training a model on content protected under an NDA and allowing access to users via a web-portal?

What is the difference OpenAI has that lets them get away with, but not our hypothetical Mr. Smartass doing the same process trying to get around an NDA?

Well if OpenAI signed an NDA beforehand to not disclose certain training data it used, and then users actually do access this data, then yes it would be problematic for OpenAI, under the terms of their signed NDA.

Yes, a tool that they charge me money to use.

Just like any other tool that can be used to plagiarize, Photoshop, Word etc.