It is my understanding that Clinton's was a public and legal payment to settle a civil lawsuit in a court proceeding, but I can be wrong, of course. Per the AP article: "By comparison, the payment in Trump’s case was through a shell company and reimbursed by Trump, whose company logged the reimbursements as legal expenses in the final weeks of his 2016 presidential campaign."
Of all the legal cases facing Trump, it has always been my understanding that this case was the weakest for the prosecution to argue. I have no clue whether this is actually the case, or not, as I'm not a lawyer.
I was not expecting guilty on all 34 counts against him. I figured some, but not all. I was surprised by that.
Public or private doesn't make a difference. For example, there are literally thousands of civil cases settled every day without the filing of a lawsuit. Part of that settlement at times even includes a confidentiality clause.
Holding and shell companies are a setup shared by every single business with assets. The concept is to keep the assets in a company that never has legal exposure while shell companies have all the exposure and none of the assets.
It's a business transaction that happens literally 1000s of times a day. It's happened untold times in the past with political candidates.