The difference is I don't ask her to do it, and I don't broadcast what I'm doing to end up on a list. It needs to be done so I do it. If you keep tally you will not have a good time either way.
On the other hand stuff I don't need or want moved (my work stuff in my closed home office) always gets "ordered" according to her standards so I have my doubts about whether much of that behavior is society's fault or some people's innate wish to see some things done a certain way or in a certain order. It has to be done based on an internal list of needs or ideals, not because society says my stuff has to be ordered by her standards.
When you're substantially better at something just do it. Your partner will do the stuff they're better at. The rest gets split or shared with a simple prior arrangement. If the result is what matters don't get stuck on the how. And if something doesn't need to be done, don't do it. You'll expend mental and physical energy for no good reason.