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If there is no significant difference in the velocity and you get a difference in the point of impact the reason becomes more ...elusive.
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I beg to differ. Okay, I differ just because I'm different.
Muzzle rise is a factor of two things, mostly. Recoil and the angle of the recoil impulse vs the "tipping point" for lack of a better term.
Recoil should be measured by Ft/Lbs of momentum rather than Kinetic energy. It's the only way to examine how much force is actually transferred from the light high speed object to the larger, low speed object. A 90 grain bullet (ordinarily a .380 bullet) could probably be cranked up to fired at the same velocity of a 158 grain .38 special or even a .357 or much higher and still not generate the proper momentum to create the same amount of muzzle the heavier bullet. Now will the heavier bullet leave the muzzle at a different time and mess up the equation? No, it's going to leave the muzzle at exactly 900 fps, as will the 90 grain bullet.
So we have two factors that with other things equal can affect muzzle rise and hence vertical shifts in POI.
And then we add in the elusives.
BTW, bullet shape doesn't matter a bit if the velocity and weight are not altered. The thing will exit the barrel at the very point as an equal bullet of another shape, and when that bullet is a fraction of an inch past the muzzle, that bullet is on its merry way and will not change it's predestined POI.
I'm discussing these as being a matter of pistols fifty to 100 feet. Not hundreds of yards
Momentum creates recoil and the recoil acting on the fulcrum causes muzzle rise.
This determine the bullet's position when it leaves the barrel. You should be able to take a contender and using different barrels of equal weight and length fire bullets of identical momentum and have these barrels all shoot to the same POI relative to the axis of the bore when fired.
Of course as you said, there are the "elusive" and small factors that can still influence the POI at longer ranges. (I refer to them as the 'PITA factors' or 'that stuff that I forgot to think of')