I think caliber makes a difference. The sample size is too small for it to become measurable.
Even a .22 rimfire can and has been used to kill the largest bears. Where it makes a difference is the potential target size is very small and the caliber does not allow much error.
A .44 magnum allows potential body shots and can break big bones.
That difference only comes into play in a tiny number of cases.
As most people who carry handguns to protect against bears carry relatively powerful handguns, there is not a huge sample of small caliber cases to examine.
A 9mm with the best penetrating loads does pretty well. It becomes a tradeoff between controlability, number of shots, and per-shot damage.
Shot placement trumps most other things.
[[Even a .22 rimfire can and has been used to kill the largest bears]]
A neighbor killed a bear with 22. Not advisable, but can be done. Poachers in our neck of the woods use 22’s on deer. Cam3 across 3 dead does, all shot with what looked like .22. The poachers musta got scared and fled, probably wqn5ing to go back at night and retrieve them.
“I think caliber makes a difference.”
My guess is noise and surprising pain makes MOST bears decide to break off an attack. A bit like a skunk spraying them. Unless the bear is REALLY angry or defensive, in which case a 44 magnum probably won’t do much.
A guy I knew working in Alaska was required to carry a .375 H&H Magnum rifle. If you want to do serious damage, that’s about as small as I would go.
I seem to recall a thread here years ago where a problem bear was killed and found to have been carrying a number of 9mm slugs.
I do not recall if the slugs were from the same gun or different guns but the writer's presumption was they represented cases of successful deterrence since there were no known cases of dead/missing humans in the area.