I don't have a clear idea on the ways these two similar-sounding words differ. The dictionary definitions aren't that helpful in this regard.
I read once in some spiritual book that it is written in the Bible: "Man has complete dominion over nature and other creations of God..." or something along those lines, and that 'dominion' means stewardship. At first, I thought "dominion" was the noun form of "dominate". Again I googled the term and found that my guess was right. Yet, the book says 'dominion' means stewardship. And supervising something is not quite the same as having a dominance over something, is it?