Like I said sophistry. But here is quick summary not all rule violations are cheating but all cheating violates rules. Ponder that conundrum.
As to Aquinas I suggest the Summa Theologica in the original Latin. I could at one time read Latin.(Unfortunately I lost my copy somewhere between our move from Spain to Kuwait. Or was it between Suriname and Spain, we moved so often it is difficult to recall and was 40 years ago. In any case it so hard to keep up one's Latin fluency these days as there are no ancient Romans around. And those that are all speak Italian, Castellano, or one of the other romance languages)
But it was a paraphrase not the actual quote.
Finally because man is a fallable being cheating takes place in all sports which is why there are referees and commissioners empowered to enforce the rules. These commissioners suspend and ban players as the need arises. So obviously these officials spend a lot of effort to distinguish between the cheaters and non cheaters. So clearly they think there is a difference.
(BTW I fibbed while I did study and could read Latin at one time, I read the Summa in English. The Dominican who taught Aquinas said we could so it wasn't cheating. It was a philosophy class not a Latin class.)
I know that does not answer all your questions but I had fun writing it.