A trade requires two sides and consideration moving in both directions. Three documented arrangements meet that test. Several commonly cited examples do not — and this page says which, and why.
Analysis of this administration frequently describes any action followed by a benefit as a transaction. That is rhetorically effective and analytically wrong, and using it would make the three genuine exchanges above easier to dismiss.
Dropping a claim in return for consideration is what settlements are. Companies do it daily to avoid legal costs, and none of the three arrangements above is unlawful on its face.
What distinguishes them is who sat on the other side. In the IRS settlement, both parties were the same government, and the official approving it for the government had been the president's personal defence attorney. In the media settlements, every payer had significant business before federal regulators, and one received a major approval weeks after paying. In the pardon sequence, the beneficiary's company had supplied the technology underlying a family venture.
None of that proves an improper exchange in any individual case. Taken together it describes a structure, and a structure recurring three times is the finding this page exists to state — no more than that.