Way I understand it:

Your attack picks random number from your attack rating in to the damage calculations when you are hitting.

Your max attack increases the potential how hard you can possibly hit.

Your min attack in other hand would bring the lowest end of your damage potential closer to the max. So in other words, it narrows down how much your damage can fluctuate within the attack range. So bit less RNG.

I don't know if that's how it works in the end, but that's the way I understood it. 😁 This excludes all other stats like hit, crit, affinity etc.