Yes there is a real world difference. Legal minimum in some African countries for some big game animals is .375.

Also IMO a 9.3x74R is weaker than a .375 H&H Magnum by a significant bit. Judging by recoil alone. At the hitting end, never been at that end! Animals die by both. I have both of these. I do not have currently a .375 Flanged Magnum and per the books, it is loaded lesser than the .375 H&H Magnum.

Now if someone wants a gutsy .375, get a Veryney-Carron DR chambered in .375 Verney-Carron. I would be tempted to get one, but it is powerful and it would be a choice between a gutsy fast .375 Verney-Carron vs a .375 Flanged Magnum in a lighter more handy DR. Which would also be less brutal on medium game.

My attitude with gutsy calibres ie high velocity for calibre, is in a big bore, instead go to the next calibre sizes up. Eg why both with a cracker fast .450, go for a .500 instead. But a .375 is often thought of as a dividing line between smaller/medium bores and big bores.