The two axis, roll and yaw, are interrelated. Bank a normal airplane and it will also change heading. Depress a rudder pedal and it will also induce roll/bank.
The roll axis of the autopilot focuses on its assignment, either to keep the wings level, an assigned bank, or most common, maintain a selected track, heading, or course (Nav). Every time the roll servo makes a correction to accomplish its assigned task, there is inherently a change in yaw as well.
The yaw damper is different. It’s primary goal is keeping the rudder ball centered (that is how it is calibrated). It’s secondary mission is to dampen externally induced oscillations.
The two work in concert for a primary goal of “driving” the aircraft where you want it to go, and secondarily, keeping the aircraft as aerodynamically straight as possible for efficiency. An “action” by one axis will result in a corresponding “reaction” by the other. An external application of force, like an imbalanced load, affects the actions of both.
To really get into the weeds, an aircraft with centerline thrust should do fine with a yaw damper without the need for rudder trim. Assuming of course, that the airframe naturally flies relatively straight. An aircraft with the possibility of high asymmetric thrust (engine loss in a twin) usually will have both merely because of the mechanical advantage difference between the two.
Rudder trim is strong but “dumb” Yaw dampers are “smart”. Pitch trim can be dumb or smart. I have never flown an airplane that had smart roll trim. The Boeing doesn’t. Just like my RV10, the roll trim in the Boeing is strictly mechanical to offset external strain on the roll servo.
Back to the OP. I removed the dumb rudder trim from my airplane when I installed the smart yaw damper system and don’t miss it at all. The airplane rides better and flies straighter in all modes. There is obviously nothing wrong with having both rudder trim and YD. It’s just overkill IMO is a straight flying single. If I ever built a twin, I would definitely have both.