I don't recall all of the details, but didn't Paula Jones *sue* Bill Clinton? (It was for that suit that he falsely testified before the grand jury, right?)
That would make the payment to Ms. Jones a settlement in a lawsuit, right?
Something done in full view of the public, right?
In 1998, Bill Clinton wasn't a candidate for anything, so it couldn't be a campaign finance violation.
There were ways Mr. Trump could have paid-off Ms. Clifford without breaking the law. A payment out of personal funds (not company funds) which was lumped into his "in kind" contribution to the campaign (ie, campaign related expenditures made directly by Mr. Trump which could include things like providing his own private plane) in a way that was legal and vague enough to not give away a recipient of payment.
Instead, Mr. Trump used the funds of his business to repay his lawyer, Mr. Cohen, for a payment he'd already induced and recorded the payments as legal fees. In doing so, he induced the business and Mr. Cohen to make illegal campaign contributions and made false entries in the official records of the business. Those false records are the charged crimes and frankly the case is pretty cut-and-dried. The falsification of the records in pursuance of another crime (campaign finance fraud) turns those false records charges into a felony.