My two cents - miraculous should be so unlikely and surprising that it's shocking when it happens.
Scoring late, then recovering an onside kick, then scoring again to win (what could have happened at Alabama) is miraculous. The Kick Six, the prayer at Jordan-Hare, the Georgia Tech blocked field goal return against FSU a few years back, the "trouble with the snap" Michigan State-Michigan game, the Flutie Hail Mary, "the band is out on the field!," etc. These are plays that were so shocking that many have a name that most college football fans know and recognize as a specific game-winning play.
The Carolina wins over Clemson and Missouri were great, but in my mind don't rise to that level of shock/awe/surprise. I was in the stadium against Missouri. It was a real letdown when the Tigers scored late to take the lead on 4th and long, but I told my wife before the kickoff that they left too much time on the clock. And then when we did the trick kick return to Harbor, though it didn't really result in anything crazy, it gave life to the stadium.
Those wins were special, but it's not like they were unprecedented or something so crazy that general college football fans were going to stop and say wow.
I was shocked with how both of those games ended. and, of course, I'm looking at them through the lens of a Gamecock football fan and evaluating them against our own history.
QB TD scrambles on 3rd and 16 from the opponents 20 yard line don't grow on trees. Then a shoestring INT to seal the win after the opponent had sliced through our D like a scalding knife through butter for what appeared to be at least a game-tying FG. Let's be honest. Who here had "QB TD scramble on 3rd and 16 from the Clemson 20 to take the lead and, on the ensuing Clemson drive, a shoestring INT to seal the win after Clemson had driven 57 yards in 56 seconds to get in easy FG range to tie the game".
Against Mizzou, we held them off all game before coughing up the lead for the first time with just over a minute left in the game. I mean, come on, be serious. What likelihood did you think there was that we would drive the length of the field in 1:10 to take the lead? I told my wife multiple times after the game "we just don't win games like that". We cough up the lead late and then lose. We don't cough up the lead late, then go on a 70-something yard drive in 47 seconds to win the game.
You give examples of individual plays. My use of "miraculous" encompasses the final outcome and multiple plays/series. And also our history. I've seen us lose games like that time and time and time and time again. Given the situational aspects of each game, these are certainly 2 of the more improbable wins in our history. Historically, these are games we simply DON'T win. I don't see what's wrong with admitting that. It speaks to the character of the team.
If you made a list of games over the course of our entire history where we were in similar situations (score, time left, field position, opponent ranking etc) and we came away with a win, I can guarantee there are less than 10 on the list. From our entire history.
After watching us coming up with new and innovative ways to snatch defeat from the jaws of victory too many times to count over the course of our history, I'll stand by my use of miraculous to describe these outcomes.